I bet the Mexican police will catch him. An American guy with no visa, a young girl, and handguns are is not welcome in Mexico. There is a good chance that one of his new neighbors in Mexico will tell the cops that there is a suspicious illegal alien in the area.
We don’t know that he does not have a passport and remember he was well planned out for this. He may be able to produce one if asked.
It’s her that does not have a passport and even that I’m not sure of. If he thought out every thing then say may have one too.