Social Security no way, but a drivers license OTOH makes sense. Make them use a REAL address so they can be located more easily if they break the law of have a wreck. Make it a "provisional" license which means it's not permanent.
I don't like illegals in this country any more than you do, but they are absolutely necessary to our economy, especially our fruit industry. A way has to be found to let them do the jobs they come here to do without harassment.