A little knowledge, so they say, is a dangerous thing. It is commonly noted that the phrase "as well as" + [noun] is 'parenthetical'. And, indeed, this is sometimes true. It is this fact, aided and abetted by dreary prescriptive usage guides that motivates the guidance, frequently seen, that the noun after as well as should have no bearing on the agreement of the following verb in examples like the OP's. However, a visit to a modern, reputable and vetted grammar source, such as the world famous and awe-inspiring, Cambridge Grammar of the English Language by Huddleston & Pullum (et al), 2002, will reveal a more complex and interesting story.
They, as well as usage guides such as the Merriam-Webster's Concise Dictionary of English Usage, point out that as well as is sometimes a co-ordinator. To make this clearer, we should say that there is an altogether different lexeme as well as, which is homophonous with the parenthetical phrase as well as. The so-called parenthetical one, is actually a two-word adverb followed by the preposition as and whatever complement this preposition takes. The co-ordinator is a three word co-ordinator.
Now the co-ordinator as well as functions similarly to the co-ordinator and. There are all sorts of syntactic tests we can do and observations we can make to show that this item is a co-ordinator. One important aspect of co-ordinated subjects is that the co-ordination counts as plural in terms of its contribution to the number agreement of the verb. So we see for example:
- Bob and I are very happy.
We don't however see:
- *Bob and I is very happy.
Neither do we usually observe:
CaGEL (2002, p. 1316) give the following real examples showing as well as used as a co-ordinator. Notice that the noun phrase co-ordinations cause plural verb form agreement:
70 i. b. _[Abstraction] [as well as impressionism] were Russian inventions.
70 i. c. _[Both increasing ewe liveweight,] [as well as liveweight at mating,] influence ovulation rate and lambing performance.
In the examples above we see the plural verb forms were and influence, not was and influences - just like we would see with the co-ordinator and:
[Abstraction] [and impressionism] were Russian inventions.
[Both increasing ewe liveweight,] [and liveweight at mating,] influence ovulation rate and lambing performance.
They, however, also give sentences where a homophonous as well as phrase (which includes the following NP) functions as adjunct:
- 70.ii.a Beauty, as well as love, is redemptive.
Note that it doesn't seem to make any difference when the as well as section is marked of by commas. Merriam-Webster (p. 102) give the following example from the New York Times, where the phrase is delimited by commas:
- He, as well as the producer, Jack H. Silverman, are Broadway newcomers.
So, in short, it would seem that either:
- She as well as I is tired of the work
- She as well as I are tired of the work
... should be ok. Bear in mind, however, that their structures would actually be very different. Having said this, the fact that the two subjects are pronouns makes the second version considerably preferable to the first. The combination I is is particularly nasty, and jarring to ones natural ear. Only dimwitted, slavish adherence to prescriptive usage guides could make one prefer the former.
Now, having said that, let us also bear in mind that given that the structures are only superficially similar - even if similar in meaning and similar in the audible or visual sequence of words - one might be better off choosing an altogether different wording for this sentence. Let's face it, neither is particularly elegant. The highfalutin effect of as well as is slightly kiboshed, imo, by the pronouns and the short sentence. There are other emphatic devices that we may want to use - especially if we have a prescriptivist "grammar"-nazi for an editor!
Edit note: many thanks to F.E. for suggestions and the MWDEU citation.