Intuitively that sounds correct. But keep in mind that the Reagan Amnesty turned 3.5 million illegals, who had not followed the law, into legal voting citizens. There have been 7 mini-amnesties (245i) since the Reagan Amnesty that have given citizenship to a few million more illegals who did not follow the legal process but who got citizenship anyway. It would be hypocritical for these many beneficiaries of amnesties, having benefited from them personally, to now oppose them for the current batch of illegals.
That is the big problem with amnesties; they just beget more illegal immigrants who believe there will be future amnesties, and the more amnesties we give, the more voters there are who will support them in the future. They are now a political force that the Republicans believe they have to hispander to.
Good, yet crappy and depressing, point.