It is my understanding that the TSA is now cross checking everyone who has a foreign address on their FAA certificate to make sure that when they obtained said certificate they were here with all visas and paperwork correct and therefore did it legally. I'm not sure how far back this goes, but is certainly true for the past few years.
This came to light after a couple of TSA agents visited a local flight school after they discovered some discrepancies in paperwork. However I don't know what happens to you or your certificate if you did it 'under the radar'................