It depends on what you mean by “correct”.
As others have confirmed, your method of removing the other coordinated noun phrases, then checking if you have the correct case for the single remaining pronoun generally gives the “correct” result according to standard prescriptive thinking. In the rest of this post, I'll refer to this as “prescriptively ‘correct’ ” to avoid confusion.
As Ron Maimon argues, this rule is arguably not “correct” if we define that as meaning “in accordance with the underlying system of grammar that native English speakers naturally acquire”.
Prescriptive rules for position and case of pronouns
The following two rules for prescriptively “correct” pronoun use are widely endorsed today:
“Pronouns connected by coordinating conjunctions such as “and” or “or” should be put in the same case that a lone pronoun would have in the same position.”
Endorsed in “Excuse me, Mr. Trump!” [Grammarphobia]. This rule applies to all pronouns equally, so the application of this rule to “I” vs. “me” is exactly the same as the application to “we” vs. “us”, “he” vs. “him”, “she” vs. “her”, and “they” vs. “them”.
“First-person pronouns should come last in coordinate noun
phrases.”
(Generally considered a rule of politeness rather than grammar, but it usually applies in circumstances where a user is trying to use prescriptively correct grammar.)
Mentioned, but not endorsed or described as a grammar rule in “ ‘Me’ first?” [Grammarphobia]; endorsed by “Grammar Girl”. As I said, many grammar “mavens” seem to view this as more of a “guideline” than a rule of grammar, but it is still widely followed in practice. The construction “I and...”, which visibly follows (1) but not (2), generally sounds quite bad to native English speakers. On the other hand, the construction “me and...”, which violates "rule" (2), generally sounds much less objectionable (which is why many people are explicitly taught to avoid using it in subject position), and some people may consider it fully acceptable in situations where it does not violate rule (1) (that is, situations where objective case is prescribed by traditional grammar rules).
(The answers to “ ‘My friends and I’ vs. ‘My friends and me’ vs. ‘Me and my friends’ ” [ELU] also cover both of these rules to some extent, although the question itself focuses on the second.)
Because of rules (1) and (2), most English speakers agree that “Steve and I attended the conference” is the prescriptively “correct” form of “Me and Steve attended the conference.”
There is a third prescriptive rule about case that is fairly widely known. Probably there are some people who would say it is still “technically correct” or something like that, but in practice people rarely follow it or recommend following it nowadays, because it often results in sentences that sound terribly unnatural to pretty much everybody:
“When using a form of the verb “to be” to link two noun phrases, the complement (the part that normally comes after the form of “to be”) should be put in the same case as the subject.”
Covered in
“Which one is correct to say: ‘It’s me’ or ‘It’s I’?” [ELU]; Grammarphobia (“How should you answer the phone?”) says to use this rule “if you want to be strictly correct,” but “in all but the most formal writing, ‘It’s me’ is now acceptable.”
This rule is sometimes thought of as "use subjective case after a form of to be" but that is not an entirely accurate formulation of the prescriptive rule. To-infinitives often take subjects in the objective case (as in "I want them to come"); this means it is possible for the non-finite form "to be" to have a subject in objective case, and in that circumstance it is prescribed to also put the complement in the objective case. Examples: "I knew it to be him" or "a man, whom I believe to be him" (The Romance of the Forest, Ann Ward Radcliffe). Prescriptivists generally argue against usages like "I knew it to be he" or "a man, whom I believe to be he".
In a sentence like “The other attendee is me,” the subject of “is” (a form of to be) is the noun phrase “the other attendee”, which is in the subjective case. Therefore, according to rule (3), the complement should also be put in the subjective case: “The other attendee is I.” This would apply equally to a sentence with coordination, such as "The other attendees are Steve and I."
But as I said, even prescriptive grammar “authorities” don’t recommend following rule (3) in most circumstances in present-day English. (There are a few circumstances where it doesn’t sound terrible. For example, in constructions such as “It is I who...” where the pronoun is immediately followed by the subject relative pronoun “who,” most people apparently still prefer to use a subjective-case pronoun: see “It is I who am at fault?” [ELU]. Apparently, some people also find “This is she” or “This is he” acceptable in the specific context of answering the phone, but others, including me, find this stuffy.)
The prescriptive rule for pronoun case in coordinate noun phrases is likely “unnatural” for modern speakers
Nicholas Sobin in “Agreement, Default Rules, and Grammatical Viruses” argues that certain “prestige constructions” that occur in English speech and writing are not, and in fact cannot be, derived from the basic grammar of the language (the system that native speakers have internalized). According to Sobin, these “prestige constructions” occur in speech mainly as the output of what he calls “grammatical viruses”, which are processes external to the grammar proper. He identifies the use of subjective pronouns in coordinate noun phrases as one of these prestige constructions, and argues that it occurs mainly as the result of two viruses that he calls the “...and I...” Rule and the “that she...” Rule (Sobin 328). The actual grammar of English is supposed to produce objective pronouns like “me” and “her” in these contexts.
Sobin argues that these rules, as speakers usually apply them, have certain properties that are not characteristic of naturally acquired grammar rules. For example, the “...and I” virus exhibits lexical specificity, in that it affects the first-person singular pronoun more often than other pronouns, and overextension, in that it commonly affects a first-person pronoun that is part of the object of a verb or preposition (e.g. “between you and I”), which should not be able to receive nominative case according to the natural rules of English grammar. (Or according to the prescriptive rules, which is why it's termed “over”-extension.)
If I understand the argument correctly, it goes like this: the fact that speakers generally use unnatural “viruses” like this to simulate the prescriptive rules for prestige constructions, rather than simply internalizing the “correct” form of the prescriptive rule, constitutes evidence that the prescriptive rule is itself linguistically “unnatural” in some way (since linguistically natural rules are expected to be acquired without any memorable effort by native speakers).
Overall, I think the main take-away point from the “virus” idea is that it seems that there are many adult speakers who have been exposed to the prescriptively “correct” forms but have not acquired the prescriptively correct rule, even if they appear to at first glance. From a linguistic point of view, what that means is that the prescriptive rule doesn’t come naturally to English speakers: unlike the vast majority of rules pertaining to English word order and case, we don’t pick it up by default in childhood.
But “unnatural” doesn't necessarily mean “wrong”
The prescriptive rule being unnatural is not necessarily inconsistent with a prescriptivist viewpoint. Assuming “natural” is the same thing as “good” is called the “appeal to nature”; this is generally considered a fallacy. Many prescriptivists would concede that people don’t intuitively choose prestige forms; if they did, prescriptivists wouldn't have such a market peddling advice manuals to linguistically insecure speakers such as you and I. (Or should that be “such as me and you”? “Such as you and me”?) I think most thoughtful people could guess that a rule that is known to trip up even educated adult writers isn’t going to be easy for children to acquire. While the natural rules of grammar are of great interest to linguists, native speakers rarely spend much time learning about them because ... they come naturally. Whether it's ever worth the extra effort it takes to follow an unnatural rule is a matter of opinion, not fact.
Ron Maimon calls the use of nominative pronouns in coordinate noun phrases “an illiterate hypercorrection”. It's certainly possible to hold this opinion, but the word “illiterate” seems meaningless here aside from its derogatory connotation: the construction is clearly widely used by literate individuals.
This is also not the way most people use the term “hypercorrection”: most linguists reserve this word for forms that are both unnatural and non-standard. The use of “NP and I” may be unnatural, but it's also widely considered to be standard in grammatical contexts that call for subjective case.
(In objective-case contexts, “NP and I” is considered incorrect by present-day prescriptivists, although it's very common (Angermeyer & Singler 186). That usage has been called a hypercorrection, but in fact, Huddleston and Pullum's CGEL argues against using the term "hypercorrection" even in that case, saying that “NP and I” in objective-case contexts is too common in educated speech to be categorized as a nonstandard usage from a descriptive standpoint.)
The specific example of “The other attendees are me and Steve”
This sentence is especially likely to cause confusion because the pronoun is in an environment where several rules might apply. According to linguists like Sobin, the form produced by the basic English grammar system would be “The other attendees are me and Steve” (or possibly “The other attendees are Steve and me,” if we assume preferences for order are due to considerations outside of the grammar).
The form “The other attendees are Steve and me” could be produced by an application of the two main rules that I mentioned (use the form that would be used in a sentence without conjunction, such as “The other attendee was me,” and place first-person pronouns such as “me” last).
The form “The other attendees are Steve and I” could be produced in either of two ways. It could be the result of the two main rules mentioned above plus the third, less commonly applied rule about matching the case of a predicate nominal and its antecedent. Or it could instead be the result of the process that Sobin calls the “...and I” virus, which would also produce forms like “between you and I” that prescriptivists have traditionally condemned.
Bibliography
Sobin, Nicholas. “Agreement, Default Rules, and Grammatical Viruses.” Linguistic Inquiry Vol. 28, No. 2 (Spring, 1997), 318-343.
Angermeyer, Philipp S. & Singler, John Victor. “The case for politeness: Pronoun variation in co-ordinate NPs in object position in English.” Language Variation and Change, 15 (2003), 171–209.
Other relevant sources that I found after writing this post:
