No, it is not possible to fly as pilot in command in a HI registered aircraft with a JAA license stright away, you have to go through either two routes
1. A permanent convalidation based on your JAA license for non revenue (private) flying to act as a pilot according to ICAO annex 1. simple, straightforward procedure.
2. A Temporary - Company sponsored validation to act as a pilot in revenue flying for the essential time needed determined by the authority. more complex, and unless a company is really in need no AOC holder will do this just for fun.
Hope it helps.