I'm not personally a believer in the whole dry drunk concept. For some unabashed flaming on the topic, you can check out what stinkin-thinkin has to say about it. Admittedly, they're a very anti-AA group.
Dry Drunk – Stinkin' Thinkin'
But since "dry drunk" is an AA concept, not being a "dry drunk" probably means doing AA and following their steps.
Getting away from the "dry drunk" label, I think it's true that getting sober doesn't necessarily make you a better person or fix the problems in your life. Working on that is important for everybody.