Cross checking your altimeter on an LPV serves exactly the same purpose it does on an ILS. If there is a substantial difference, more than 100 feet, you should figure out what is wrong. It could be a misset altimeter, a bad GS indication, or in some cases just temperature. It is a test of reasonableness and goes with best practice of intercepting the GS from below and noticing that this is the case. So what would you do if the altitude was off by 500 feet? Yesterday on an IPC, a pilot flew the ILS with a centered GS the entire way down. Turns out, the GS was flagged and the indicator was in the center. Never noticed a fly up transitioning to a GS intercept. The GPS was set to GPS and not VLOC.
Baro altitude is not compared with GPS altitude on an LPV approach. Pressure altitude (not MSL) is used by a GPS as an aid to RAIM determination, but with a WAAS GPS in the WAAS service area, RAIM is not being used. Even where it is used, it is not a cross check for altitude, but an additional input to determine if the lateral position is satisfactory as it can be accomplished with 4 satellites instead of 5.