Well, it worked for me in Phase three, although by the time I tested it, I was done with the main scenario and was catching-up on sidequests only.
Most of your quest experience comes from sidequests rather than the main scenario, so it is certainly viable to pump up a non-combat class with quest experience.
(Point of interest, class quests would not let you do them with a job equipped. You had to be playing as the base class.)
