Not flying on CAP's but elsewhere in JAA-land, and we do the same.
Logging it as P2 because:
The RHS pilot is type rated but not yet qualified by operator to be SIC until released for being so. That means without third pilot on jump seat, the flight can't depart legally. The only qualified SIC is the pilot on the jump seat, therefore s/he will log it as P2.
To be compared by the line checkers, who is not required to be onboard for the flight to be legal. They are not part of operating crew and therefore no flight time being logged. And funnily enough not even counted as FDP (only DP).
Every operator has to keep a log of each pilots. If you are unsure you could just ask for a printout and see what they logged on it.