However, like Fuji and IO have seen, once you do the temperature correction so you know what the altimeter meant to tell you! an IFR GPS (particularly one with TAWS) will give a very good true altitude
I think you mean EGNOS or WAAS, but yes that's about it. GPS altitude is much more accurate than most people think, or were taught to think - assuming the GPS is a decent one. All the IFR units contain a table of geoid corrections for the earth's surface so they do display true altitude above mean sea level.
GPS is much less accurate vertically than it is horizontally
Not "much less" if it is a modern IFR certified unit. There are cheap GPS receivers - I have one here, with the SIRF 2 chip - which have a constant 200ft altitude error in Europe.
where exactly he might be that he cannot get a QNH
There are lots of places where the only way to get QNH is to call up ATC at some major airport (and they might not appreciate it) or to dial up the ATIS (if it exists; many big airports in Europe don't have ATIS). In the UK you have the regional pressure setting which everybody knows is usually inaccurate, though it should give you a "worst case" altimeter setting for terrain separation. It definitely cannot be used for vertical separation from CAS.
Europe does not have the American 18000ft transition level. It varies all over the place, and in CAS you can get a different value issued to you anyway.
Everybody, myself included, knows that barometric altimetry is the accepted standard for
traffic separation, but I post this stuff just to make the point that GPS altitude is the height above mean sea level to a reasonable accuracy.
After all, all commercial GPWS systems use GPS altitude which they match against a terrain map. They can't use the baro altitude because the system has no way what the local QNH is, and if it did use it it could not be sure whether the pilot has dialed the wrong value in.
I always check the GPS altitude (on both my IFR KLN94 and the Garmin 496 which usually uses EGNOS for additional accuracy) against the altimeter before flying an approach, and if I had a big discrepancy I would re-check the QNH, and if this was still wrong (which I have never seen) then I would head somewhere with an ILS.