I don't think it's ever been mentioned, though Hevvy does have a human face and lately her look has become more ..."organic" (when we first saw her she seemed to have a snakelike body covered in scales, but in recent chapters, she looks more like she has a mane. Dunno if that's a continuity error or if Hoshino's trying to sneak in something.) Plus the only Exorcists we know of are all human. That doesn't mean that it's a mandatory prerequisite though.

*suddenly has a vision of an Exorcist squirrel* *dies*