The U.S. was generous in giving American citizenship to the Mexicans who remained in the territory we took over in the 1800s. Mexico, I don’t think, would be that generous if they took over our areas.
According to Mexico laws LEGAL immigrants have loads of restrictions on them, for one they may not own property on water; ever. Their kids will not automatically be citizens. Lots more. Plus if you are caught there illegally you will be in a mex prison for 2 yrs; a death sentence for a gringo.