I suspect they will get around to having a time limit on these proceedings, and if they can't get to them in that time, then the immigrant is deemed illegal. Frankly, I think they could remove 99% of them by questioning them them on the spot, and making a snap judgement.
If Trump tries to do that, then I would expect the Dems to filibuster it. And if it is done by executive order, then the next Dem president would reverse it. Don't you agree?