All the feedback I've heard says don't but synthetic fluid in the transmissions unless you are operating at extremely high temperatures, that the GM A4 runs best on regular GM approved transmission fluid. I believe the Mobil differentional fluid requires the addition of a friction modifier, thus I only use Mobil in my differentials that don't require FM. If that is confirmed, consider using Royal Purple GearMax. It has the FM already mixed in and has good reports from other GTO users.
05 Brakes w/ C5Pads, K&N CAI, TBCoolantByPass, -CAGS, , +Outlets, DeadPedal, UnSpoiled, GasCapHook, PedalsRightSideUp, HitchToGo,