Maybe, but my impression is that they weren't mages even back in Elvhenan. It's just that they were able to manipulate things in the Crossroads. It isn't that everyone was a mage, just that everyone could manipulate the magic of the Crossroads dimension. Like Sandal's prophecy about the magic coming back, all of it, then everyone will be like they were. The Fade's magic would simply reflect the mind. Anyone could do it. No mana required.
Also, to the discussion above, Battlemage and Knight Enchanter use magical spells that are geared toward battle. An Arcane Warrior focuses magical energy inward so the mage can wear heavy armor and wield real weapons as any soldier would. It also grants better defenses against melee. So it is different from the other specializations.