If you're an alcoholic, you'll soon have bigger problems than whether or not you should join a band. I always recommend to new people something like this: Forget about the drums, friends, career etc (what will happen afterward) and concentrate on quitting and staying sober.
You mention CBT. Does that mean AA is out of the question ? It worked for me, and millions like me. You're probably going to find quitting drinking (and staying stopped) is a LOT harder than quitting pot.
If so, you can check out the secular connections here, and they can tell you about SMART, LifeRing etc.
Good Luck and God Bless