We were caught out this way, we went for some hour building at LGB, and my mates licence hadn't arrived in time. The FAA FSDO issued his temp airmans certificate no problem (you need your CAA licence number to get this...), but as this is only valid in conjunction with the JAA PPL then it was effectively invalid. As he had a student permit from before, he was allowed to fly on this but SOLO, and remember that the instructor has to endorse your cross country routes on the FAA student permit. Every time we carried PAX I had to be PIC according to the law as I was effectively the only one with a valid licence.
Depending on how long you're off to the states for, the CAA may send your licence out to California...