That is part of current immigration law and any President will have to follow it unless the law is changed.
In the past that part of the law was used as a carrot to get illegals to agree to be deported immediately and not clog up the courts. If they agree to be deported they may apply to return legally in the future. If they insist on a court hearing and lose they may be barred from ever legally entering.
The truth is just because they can apply to return there is no guarantee they will be able to do so.
I can only go by what Trump has said with his own mouth. And thats not what he said.