You would get a Class 2 min. JAA medical before starting your PPL (Class 1 if professional licence), your training at the JAA approved US school would be as if it was in the UK. You would need a FAA min Class 3 to fly solo in the US, but this is far less stringent then a JAA Class 2. You would submit your application to the CAA for your JAA PPL in the same fashion regardless of whether you trained in the UK, or at a JAA approved US school.