When transformed into a Watcher in the Filer's Wing, you cannot drink potions. However, if the player is an Argonian, attempting to use a potion will still heal you due to the Resourceful passive, which recovers Health, Magicka, and Stamina when you drink a potion.
You can't recover health infinitely--it seems that you can only recover health periodically, possibly on the potion use cooldown, even though no potion is actually used. I haven't timed it exactly.