For numbers between 1000 and 9999 is it proper English for the word "hundred" to be used? For example is it necessarily wrong to say "eleven hundred" when referring to 1100?
You can say:
one thousand, one hundred.
Both are correct.
The number "1100" may, depending upon context, most reasonably be read as "eleven hundred", "one thousand one hundred", "one one zero zero", depending upon what it represents. Some things are typically counted in groups of 100 (e.g. years), and some things that appear to be a single number actually represent the concatenation of two numbers [e.g. street addresses in the US combine a block number with two digits that identify an address within a block] or four numbers [e.g. digits of a "telephone number"].
If a four-digit number is written with a comma between the hundreds and thousands place, it should almost generally be read by describing the number of thousands, and the number of things beyond that [e.g. 1,234 is one thousand, two hundred, and thirty four], except as noted below. For numbers without commas, I would suggest the following [N is 1-9, X and Y are 0-9; HH are 11-99; excluding multiples of ten, and II are 10-99]
0000 -- zerozero, zerozero 000N -- triple-zero N 00N0 -- double-oh-N-zero 00NX -- double-oh-N-X N000 -- N thousand N00M -- N thousand M N0II -- N thousand II or ten/twenty/thirty/etc. II HH00 -- HH hundred HH0N -- HH oh N HHII -- HH II
Note that leading zeroes generally only make sense for things like phone numbers. The other formulations are applicable to years and addresses as well, and the N000 and HH00 are suitable for use when counting things whose counts multiples of 100.
For numbers that represent counts of things (but do not represent calendar years like 1980 or 2014), it is reasonable to use the two-digits-plus "hundreds" form of counts if all other counts with which it might logically compared are only expressed to two significant figures. If bins have 450, 1,100, 2,000, and 5,700 items, they might be read as "four hundred fifty, eleven hundred, two thousand, and fifty-seven hundred". If, however, the quantities had been 453, 1,100, 2,017, and 5,706, then they should be read as "four hundred fifty-three, one thousand one hundred, two thousand seventeen, and five thousand seven hundred and six". Even though the second number happens to be a multiple of 100, it should be expressed in the same form as the others.
Both are fine if you remain consistent, if not you will discover:
eleven thousand eleven hundred eleven = twelve thousand one hundred eleven
Context matters, and seems missing from the question. I’d suggest that “hundreds” flows from years pronounced this way. 1776, the year, is pronounced “seventeen seventy six” and 1800 would follow the same pattern, going with “eighteen hundred” and not “one thousand eight hundred”. Even for a box of 1,235 buttons, I’d imagine a student using the ‘year’ pronunciation and saying “twelve hundred.....”.
The truth (to me) is that as long as the listener understands what you mean, either way is fine.