Technically all a Heartless is is a heart overwhelmed by darkness. The name 'Heartless' is more a play on words than a literal description. Xehanort named the creatures Heartless because they were 'apparently' devoid of hearts. However, if you notice when Sora becomes a Heartless, his body disintegrates, his soul forms Roxas, and his heart becomes a Heartless. I guess Xehanort thought that Heartless had no hearts because of the lack of light there, and as all hearts have dark and light, he could come to a conclusion that they had no hearts. That is wrong, because all beings have to have at least a heart, body or soul. Since Heartless do not possess a body, or a soul (The Secret Ansem reports state that a Nobody is the soul of a being left to linger) they must, by process of elimination, possess a heart.

If a Heartless was to rid itself of darkness, it would turn back into a human, as it happened with Sora. There have been no instances of a Nobody ever re-possessing a heart- the closest thing we have is Roxas and Namine joining back with their others- but I think that if a Nobody was to re-find it's heart, a transformation back to a human would happen, similar to what happens if a Heartless rids itself of darkness.