The experience of the vast majority of real alcoholics is that it doesn't work that way. Once the alcoholism is active and present, it always is, regardless of whether the underlying stuff is cleaned up.
But we all, all human beings, have underlying stuff, don't we? What happened with the alcoholic??... well, that's how many of us learned to deal with it, we drank... non alcoholics don't, at least not alcoholically...
Mark