Atheists: Would it hurt you to try?

Certain type of people can "repent" for their "sins", not because a supernatural entity requires them to do so, but because they, as you said, know in their hearts they've done wrong, and want to make things better. If you believe that one needs to have God in his heart to be capable of such a thing, then God is simply a set of morals, a sense of right and wrong - not a creator of the universe.