Not really. The people asking the question will know he is lying, when he says "I am a citizen". There are very few good illegal alien liers.
The interviewing/interrogation techniques we use in INS are very effective. It is very easy to tell if someone is lying to you and then trip them up in the interview.
I'm considered an armature, only be working for INS since 1997, and I catch them 99% of the time.
When do you get to be a full-fledged electric motor? Do you have to score 100% for a whole year? :o)
And the problem is in how the folks saying "No ID except for non-citizens" structure it. All it would take would be a simple declaration of citizenship, and that jack-booted thug law enforcement officer has to leave that person alone from that instant on, and any further questioning is a violation of that person's civil rights.
Be advised: there is a substantial contingent on FR who only tolerates your existence as a Federal LEO because your work, of necessity, involves non-citizens. And if some of the ideas about sanctioning employers come to pass, they will hate you with 100% of their beings once a "solid citizen" gets in trouble with the INS.