He could pardon them for the past crime of coming here illegally, but if they remained in this country they would continually be breaking the law. He would have to pardon them everyday. That is, without amnesty.
Just my opinion.
That was my thought, too. He can pardon them for being illegals up to the moment he pardons them. But they will still be illegals the next day. The right to pardon is not the right to confer citizenship.
Also, I think that the power is to pardon a person. Therefore, he would have to have the names and addresses of those he is trying to pardon. Just like a criminal charge is specific to an individual, the pardon would need to be likewise.
A blanket pardon pertaining to people who meet certain fact situations should be ineffective because it would take a court action to determine if the pardon applied. How many illegals would trust that setup?