Since they would probably want to make the Blue Mage something of their own design if integrated I can totally see them using the Primals attacks abilities as the BLU's main spells/weaponskills because that's just how they roll. Could probably look at the recent Raubahn fight for some pointers. Even if personally it was basically human Ifrit and a one trick pony battle.

Raubahn's very name being a homage to the Blue Mage NPC of XI.