Do they accept foreigners looking to get a rapid test to fly back home (out of the US)? They are only visiting on a visa for vacation.

Yes, I did that, it was free and got my results in 2 hrs

Rapid tests cost money / aren't insurance based; I suspect they'll be happy to do that. You can call ahead if you're worried about it, but the easiest way to confirm is just to try to make a reservation online - if the system let's you, they don't really ask any more questions once you're there for the test.