hmmm, good question! the animal bodies he possesses are mortal, since his first cat body does die in soulless army, but it's unclear if the cat body is still capable of getting sick or injured in a normal way. i think even if he could he wouldn't be able to be treated by a normal vet - he's definitely not a normal cat! he'd probably need someone from the kuzunoha clan to tend to him, or if he was really in bad straits, have his soul transferred to a different body.