You have to understand. The check box isn’t on the ballot. Its on the registry with your name and address. If you illegally vote, you’ve basically reported yourself to the state. The poll worker is on the hook too if you check that you aren’t a citizen and they still allow you to vote.
If you illegally vote, you’ve basically reported yourself to the state.
FWIW - For an alien knowingly to make a false declaration of US citizenship makes him/her deportable - no matter what mitigating circumstances are - and that person may not be admitted back into the US. No exceptions. (That’s the law - I don’t know whether and how efficiently the law is enforced).