Depends on the level of coma one is in but generally, no, it doesn’t.
Sleep is a complicated systemic thing, for starters the brain rewires itself during sleep, actively, via dreaming and other neurochemical process. When one is in a coma one’s brain is injured so it doesnt do that.
But again there are several levels of being comatose. Does one have muscle tone? Is the stem affected? Is the pituitary and hypophysis affected? Et cetera.
For example, sleep causes human growth hormone secretion which a comatose state would not.