Basically yes - all systems have errors. Any error, however small, in the achievement of a perfect alignment of a platform will induce a false acceleration/s which will integrate to position errors over time. These are corrected in the FMC by some sort of update as you list. I don't know how good your 'GA' ones are, but if they are like the 'old' gymballed platforms we began with, you would be pushed to see any attitude error - we are talking fractions of a degree normally. It will be 'map shift' you will see plus possibly a 'residual' groundspeed on stand. Map shift is becoming a rarity in airline usage as GPS updating becomes the norm. In the 'old days' a shift of 30 nm or more was not unknown and I had one of those at the end of the Black Sea after an hour without a DME update. Didn't half screw up my descent planning into Baku
FPOBN has got confused during his 'evolution', I think, between using GPS for alignment and updating, and is under the impression that a GPS can produce
attitude information of the accuracy required for a platform re-alignment. That'll be the day! That WILL be evolution, dude.
Many people get confused between the 'gyrosopic' attitude functions of a platform and the position derived from accelerations to that platform and then displayed to the pilot.