WCollins
The altitude readout from a GPS is normally the vertical portion of the 3D GPS solution.
Over the last 200hrs I have always found it (KLN94B) within 100ft of the altimeter - whenever the altimeter was set to a known good QNH; "regional QNH" is frequently well out. This is at few thousand feet or lower; above that the error is bigger but that's most likely due to altimeter errors due do deviations from ISA.
The QNH setting, and the altitude encoder, which an "IFR approved" GPS has is for RAIM purposes. It does not affect the displayed altitude.
For what it's worth I always check the GPS altitude against both altimeters before an instrument approach. It's never been out, but if it was, and both altimeters read the same, I would have to suspect something potentially dangerous with the altimeters.
I understand why "GPS altitude" is unofficial; I am merely saying what I know about it.