Yes, the USA would surely love the fact that Mexicans could legally live in their country now.
The Union would only work with defense and trade, and perhaps agricultural and fishery policies.
I honestly had not taken that into consideration. But, before Mexico could join the NAU, it would have to meet criteria set by Canada and the United States (it is obvious these two would be the founding members, as I doubt any other nation in the North American continent currently has the same standards).