According to my research, the census does little to establish if the persons counted are US citizens. When they do, using the Census long form, lying about citizenship status would be expected.
By the way, The House can change the rules to disallow certain groups of non-citizens from being counted as part of its reapportionment process.
Either on the form or in personal interviews, whether someone is a citizen is indeed asked.
Having worked for the Census and worked in areas obviously filled with illegal immigrants, in personal interviews with such people, I never, ever, ever, ever saw any claim to be citizens. They'd say they were not citizens but immediately add "I have a green card" (whether someone is in the country illegally or not, obviously, is not asked by the Census.)
It wouldn't be remotely realistic for Census workers to actually investigate citizenship status.