Well, it's hard to say

First of all, I know that someone (an American actually) got caught by IRS and was asked to pay penalty. He was negotiating with his employer. I didn't know what happened in the end. Moreover, even if you left that employer, you may still contact them to correct it if you desire. I don't think that USCIS would care very much. But if IRS/Social Security Admin. caught you and sued you for some kind of fraud, ... It's your decision. In my opinion, you ought to pay what you ought to pay.