I don't know if there's such a thing as "settled law", but from what I'm reading (and what you've written), this does appear to be as close to "settled law" as something can get. There's 150 years of jurisprudence/precedent behind it. The only exceptions carved out appear to be people not under the jurisdiction of the US government, like diplomats, and occupying armies (which we don't presently have).

The administration would (somehow) have to get the illegal migrants classified as either diplomats or an occupying army, or something I haven't though of, first.

And, of course, that doesn't deal with asylum-seekers. That is by far the majority of migrants we have to deal with today, and they aren't criminals (or illegal). Asylum is a legal request. The right seems to forget that a lot.