No they won't, that's why this is so depressing. The only thing Congress can do is veto the agreement once it is signed, BUT there is a SCOTUS case (INS v. Chadha in 1983) that says a congressional veto is unconstitutional. So even if Congress vetos, the LaRaza crowd goes to court and enforces the totalization agreement. The ONLY way to stop it is to convince the Bush idiots this is a horrible idea so they don't sign the agreement to begin with.
To get the Social Security money, they have to have first paid money *in* to our Social Security Administration, and then they have to return home to recieve their monthly checks.
Why is making them return to Mexico such a bad idea in your world?