Will we be able to get married without him being deported?
Yes, don't worry. Getting marred does not lead to one being deported. The marriage office will not pick up the phone and ask ICE to come and pick up BF... He better have valid id, however, such a a valid national passport. If BF Mexican, a "matricula" issued by his consulate will not do and will only serve to raise unnecessary eyebrows. With a valid national passport it will not occur to anyone to ask for proof of his legal status. In any event, suffice it to know that legal status (or lack thereof) is irrelevant for marriage purposes. They cannot refuse to marry him because of that.
Please don't forget to designate a "Best Answer" to your question.