Not quite. A person without proof of legal entry can still apply for asylum and, although the immigration law may not give non-asylum seekers without documentation a defense, the President could grant them legal status under his executive power if, for example, he determined that their presence was necessary for national defense. There are other possible avenues for such executive action as well. Not sayin' it's a good idea, just pointing out that our constitution is unique in giving POTUS the powers of head of state, head of the government and Commander-in-Chief. A president can do a helluva lot more than most people realize because his restraints tend to be political rather than constitution. Trump may shift this dramatically if confronted by a hostile Congress.