I can't give you a 100% correct answer I'm afraid, but you can train for your JAA CPL on the back of an ICAO PPL....the US doesn't really have an RT licencs as far as I can remember (I have a standalone FAA PPL too) so I can't imagine you will need one at all for the CPL issue??
Things may have changed though so apologies if I'm a little behind the curve?