Different issues here.
First off, for non-precision approach such as RNP, it is non-compensated baro for the altitude, which is very temperature based. Effective Glidepath is why there are temp limits for the procedure on the charts.
Depending on the FMS, the GPS altitude is calculated different ways, but all of them relate to the WGS 84 ellipsoid, not actual terrain (HW uses a lookup table from a grid, while GE uses a calulated solution)
The Boeing FMS does not use the GPS altitude for final approach unless you have a ground based augmentation such as GBAS.