I think an admin can navigate to a user’s Preference/Profile page and amend a user field even if it’s set to be non-editable after signup. 
ETA: Just to link it up, there’s also this recent topic suggesting the user field override should be able to be performed from the user admin page rather than from their preferences Custom fields should be editable by staff. Might be worth a comment on there if you think that would have made this ability more discoverable?