So most of the time, GPS altitude will closely resemble pressure altitude [...] indicated barometric altitude
Depends how close you mean by close. It only has to be about 15 degrees colder than ISA and you'll have a difference of almost 300 ft at 5,000 ft, or just over 100 ft at 2,000. Allow a good distance from any controlled airspace if your altimeter fails and you have to use the GPS altitude...
Mark