I know they eat wool clothing, but do they ever eat it straight off the sheep?
Remember, it’s moth larvae that eat wool, not adult (flying) moths. Female moths lay their eggs in a nice cozy woolen object and they hatch out into wool-munching larvae.
But I doubt that those nice cozy woolen objects include live sheep. Most female clothes moths don’t fly at all until they’ve laid their clutch of eggs, so how would they even get to a sheep?
Yes, they eat the wool off the sheep. Not when it’s on.