>can damage from poor sleep be undone?

In time, yes, absolutely. Brain damage from something like poor sleep can be cumulative. But getting into a healthy sleep pattern allows the body to heal and stops further damage. In time, even if the damaged brain stays that way, your brain learns to work around the damaged bits, like with stroke victims. And since the damage is (relatively) minor, people can "recover" from that kind of damage much more readily than, say, stroke or accident damage.

With proper diet and rehabilitation, other damage from poor sleep is also reversed in time in most people. Weakened bones, weakened immune system, skin damage... all of that can heal with proper care.