Oh, and what I had meant to add was that, as far as I understand, you turn up in the US with your JAR license and medical and then go to the local FAA office (think you might need an FAA class 3 medical also) and they give you a 'restricted' license. It's restricted in that you're only allowed to do whatever is allowed on your JAR license (IMC not counting since it's UK only).
So the answer to your question about needing an FAA PPL is yes, but there's not a lot to getting it and no flying needed (although I guess you'll still need to do a check out before renting a plane and, for me at least, I think a couple hours practice on the US R/T and procs would be a real good idea)