Yes. There's been Supreme Court cases that say you still get due process, can't be beaten into confessions, etc. I don't know if that applies to 1A specifically, but they absolutely have some rights:
Unless you're declared an enemy combatant, or terrorist, whatever those things mean. Cf: everybody tortured or just waiting for disposition at Guantanamo since 2002. Oh and that's for citizens too.
US Citizens have rights everywhere in the world, and everyone has rights when on US soil. People who are neither US citizens not in US soil have no rights under the constitution.
America believes that all men are endowed by their Creator with certain unalienable Rights, as long as they're a couple of generations removed from immigrants and #BackTheBlue.
See sec 501 - https://www.aclu.org/other/aclu-fact-sheet-patriot-act-ii