Do people ever recover enough from major depression that they don't need treatment anymore?

Sometimes. In the case of a first episode, about 50% of patients will never have another episode. Unfortunately, the second episode means a risk of 75% that you will have another episode, and the risk goes up from there.
Yes. If the depression is the first one ever and caused by a bad situation and there is little family history of depression, there is a good chance that full recovery is possible with good treatment and resolution of the stress.