Oh yeahNO. Her classes can be Commando, Sentinel (her optimal), Ravanger and forgot the last. Just because she uses a lance does not make her a dragoon, and her dragoon-like-abilities are not sufficient. By your logic a warrior with a lance with dragoon sub is a dragoon because he is using a lance/spear and using abilities like jump.
And oh my, did you just compare Fang to Kaim? You seem to repeat your mistake once more only that this time you took a misstep and fell down a staircase. You realize that Kaim has a spear as main weapon, complete set of Dragoon AF gear, the entire arsenal of dragoon abilities, gear AND is the commander of of the Baron Dragoons. That's a hell of a lot more than what I can say of Fang.
Again, tell me how she is supposed to be relevant to this discussion. Your sense of imagination intrigues me.