By reentering without inspection after a deportation, he is not permanently barred from immigrating to the U.S., however a waiver will be available after he spends 10 years out of the U.S. You can file for him then if you choose to get married.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
There is a permanent bar against him for is actions. I really doubt this can work out, but you can most certainly try to show the equities of his case and ask.
This is an immigration issue. However, when a person is deported, there is usually a period of time that he is given not to reenter the country and not to petition for change in immigration status. Talk to an immigration specialist on this. I don't think the wedding will solve the problem.
Unlawful re-entry after a deportation is not only a criminal offense, it also technically renders a person permanently ineligible for lawful immigration status. If he were to spend 10 years outside of the United States, then he may be able to apply for a waiver of what's called "the permanent bar," if he otherwise has at that time an immediate means of obtaining lawful status. But the short answer to your question is that no, marrying him will not suddenly make him eligible for permanent residency. He has many years ahead of him in Mexico before that is even a possibility.
THIS ANSWER IS FOR INFORMATIONAL PURPOSES ONLY, DOES NOT CONSTITUTE LEGAL ADVICE, AND DOES NOT CREATE AN ATTORNEY-CLIENT RELATIONSHIP. Immigration is complicated and the wrong action can have serious consequences. Never take action in your case based solely on general information like is offered here. Speak to an attorney who can give you specific advice about your own situation.