Devil's Advocate:
Chances of him getting caught, slim to none (unless he works in a profession that is raided a lot like construction or hospitality). No one asks for documentation for interning (a form of volunteering) i.e he could ask his employer to withhold his pay till he gets his EAD. Its dishonest and in the gray area but its possible.
Please OP, ignore the remarks of two certain gentlemen and focus on what you want and what will keep you safe. The stigma of divorce is an illusion society creates to keep it functioning. If you feel you are being abused, then leave. If you think that maybe you and him have had a bad week and only need counseling, then go for that option.
Don't take the advice of anyone that quotes Full Metal Jacket like it’s a life motto.