if you do get busted as a foreigner doing illegal stuff here, you will be deported and chances are they wont let you back for a very long time.
yet then again, there are millions of illegal mexicans who do illegal stuff every single day and the police "can't touch them", if ya know what i mean.
I personally have been admitted to a very good part 141 school (1 week prior 9/11) without having a student visa. I had a journalist visa which, according to INS says i can't study here - or something like that. They didn't care cause it was valid for 5 years and let me in. Even after 9/11 i updated my visa and they still didn't care.
IF the flight school gets cought admitting foreigners in an illegal manner, they will lose their right to admit any other foreigners. I doubt it is worth it to them since 9/11.