We are not talking about green cards and temporary residence in foreign country. The illegal aliens in this situation would become permanent residents who could work but not vote. How long do you think that will stand up in court when the first one sues?
It would stand up forever. Non-citizens have no right to vote. They would have no grounds to sue. You think if you work in Canada or Mexico, but retain U.S. citizenship, that working there would give you the right to choose their leadership?