Is Itt human under all that hair, or is the hair itself a living kind of entity similar to Thing?
Gomez and Cousin Itt discussed this very point in the season 2 episode Morticia's Romance, Part I
Gomez: Underneath all that hair, you really are... What are you underneath all that hair?
Itt: [Makes noises]
Gomez: Roots? Makes sense.
The assumption (from the season 2 episode Cousin Itt's Problem) is that without his hair, he'll be without form.
Gomez: Cousin Itt, you're losing your hair.
Morticia: He's right.
Gomez: Without his hair, what is he?
Morticia: Nothing. Absolutely nothing.
Although they may have meant this figuratively rather than literally.