No, no it does not.
I've given this much thought, and have come to the conclusion that this is what really happens.
Instead of time healing the wounds, time simply deadens the nerves, deadens the feeling. The wound is still there, but it's blanketed with an anesthesia called time.
We still carry around things people have sad, hurts that we have suffered too, but time makes those things matter less and less, until we reach a point in which they may have completely slipped from our minds.
But not completely. Never completely.