There's an easy way to prove that the FPV does or does not ADC data. Pull the CBs for the ADCs (well, at least this is possible on the Boeings which don't have ADIRUs).
Why would you need long term error correction on an instrument of this nature? You want to know what the aircraft is doing now. Of course, in the case of V/S, your IVSI may be damped so that that the needle isn't going crazy, but is this necessarily a requirement for the FPV? (and couldn't it be done electronically anyway, in the IRU?)
Perhaps the pilot should not use the FPV to maintain altitude simply because of HIS/HER accumulated errors. The pilot can't possibly keep the FPV exactly on the horizon every second of the flight, so the aircraft may go up/down over the long term. By the way, how does Boeing word its warnings?
Regards
NSEU