They may not need to fill out the survey: the Feds are placing illegals where they want them and recording their locations, so as far as they are concerned, there's an accounting. You and I might not think that's a proper count, but we're also not the ones doing the tabulation.
This pertained question about tourists.
Do not think they count them, or how accurately.
But they really try to count all illegals, and all resident non-citizens.
Taking them in account in congressional, but also state districts boundaries determination is based on some old supreme court decision (actually on interpretation of some SC decision).
This would be OK, if the non-citizens were distributed uniformly around the country.
But they are NOT!
Noncitizens, and especially illegals tend to congregate in small, well defined areas, mostly among minority citizens. So Rep Nydia Vazquez (D-NY) represents only about 200,000 citizens, a lot less than average reps with about 700,000 citizens.
She gets reliably reelected for many years. If you look at her voting tally, She ends up with ridiculously low number of total votes! But they are mostly Democrats.