Ian W
We are also now in the position that ATC surveillance is based on GPS (or rather satellite based positioning - includes GLONAS, Galileo etc.). As it is one of the little recognized aspects of the move to ADS-B and C reports for the basis of aircraft tracking that the Air Navigation Service Providers are now becoming reliant on GPS.
On the horizontal plane, absolutely ,( GNSS is the "politically correct" term ), but the altitude part of ADS is still derived from Mode S transponder altitude, whose encoder is barometric, and unlikely to change in our lifetime if you ask me .