It's very not cool to set an altimeter against the GPS altitude.
GPS is much less accurate vertically than it is horizontally and so GPS altitude may differ from true altitude by hundreds of feet. With a typical decision height of 200ft AGL on an ILS, that error could be enough to kill you.
Aviation altimetry is based on indicated altitude above a datum. For QNH the datum is sea level but except in perfect ISA conditions the indicated altitude above the sea level datum will not equate to true altitude because of temperature error. Temperature error affects altimeters equally (but of course not GPS) so indicated altitude remains the correct and reliable method of providing separation. Above transition altitude the standard pressure setting of 1013 is used, which introduces a further deviation from true altitude equivalent to the vertical difference between the datum 1013 pressure level and sea level.
In short, indicated altitude and GPS altitude can potentially have significantly large differences. Except in extreme weather, any QNH from within the last 6 hrs or 200 miles will probably be much more accurate than setting the altimeter against the GPS. If you can't obtain a QNH less than 6 hrs old or from within 200 miles you're doing something wrong.
Of course, sometimes the GPS alt will match the pressure altimeter perfectly, just as a stopped clock tells the correct time twice a day.