Mexico would start out as a territory or protectorate, with no electoral votes (like Puerto Rico). The transformation of the corrupt government would take time. But we could reap huge benefits from the natural resources that Mexico has, not to mention the huge benefits to the Mexicans themselves. They obviously have no clue how to run an honest government.
And, No, not all cultures are equal. Our American culture is unique, special, worth preserving, worth fighting for, and better than ANY other culture on the planet, now and in the past.
If it ever happened I think it would happen just like you are saying.
(Of course a sizable chunk of them are already voting her illegally anyway.)