I’ve heard anthropomorphic dragons referred to as “scalies” (as opposed to “furries”). So, they’re not, but it’s the same thing, just a different kind of creature.

I would say that for any furry who dresses up/has a fursona, the choice of the specific animal is a personal one, and, despite the name, it isn’t limited to foxes, dogs, cats, wolves, and the like (e.g. furry species). Teenage Mutant Ninja Turtles had my generation and the next couple wanting to be turtles for years. “Heroes in a half-shell!” And while Skyrim popularised the term “Dragonborn,” the name existed prior in D&D as an actual race of anthropomorphic dragon men (and women) with breath weapons and all. Just not wings. Sometimes tails.

So… the scalies always were. As for whether or not they belong in the furry fandom… tis not for me to say. I’m just a fan, though I do have a cosplay that is furry-adjacent (Tom Nook from Animal Crossing).