With the GPS's i've had in GA so far, any that never had their databases updated (Which was most as honestly it wasn't really necessary and we never had any problems) were placarded as being "DAY VFR ONLY" or something to that effect on them or in the case of the Bendix Kings used in Airvans it was actually a message on startup that it was for VFR use only. I should mention that these ones were of course installed in the Aircraft not handheld.
Mach E Avelli, in the only Aircraft i've flown IFR that had a GPS, we regularly did the update, can't remember anyone having to be specifically trained or approved for it, of course we were shown how to use the Garmin Update Program beforehand and it was often flown out-of-date on VFR operations, not IFR, sometimes it would just be busy or end up away from base for a few days and go out of date. I can't remember the MR ever having any entries related to the GPS being updated, that info was kept on a board in the Chief Pilots office and as usual Pilots required to check before flight, both board and GPS, never had CASA say anything about this to us.