I think what happens is that your JAA PPL will be replaced by your JAA CPL, but the license number will carry over. That would mean your FAA PPL is now based on your JAA CPL. In that case you don't have to do anything. In a Euro-reg aircraft you can exercise CPL privileges, in an N-reg you can exercise PPL privileges.
But if your license number somehow changes (at least the part of the JAA PPL/CPL license number that's listed on the FAA PPL) your house of cards comes crumbling down. That's the disadvantage of the whole piggyback thing.
An FAA CPL piggyback based on a JAA CPL piggyback is a completely different ballgame though, compared to PPL.