Firestorm,
I tried to deal with 'my problems' of depression and anxiety for a couple of years before I got sober. Real serious can't get out of bed depression interrupted with panic attacks. Like others have said, these issues may be difficult to treat while living with active alcoholism.
Do what you think you have to do. For me, when I took the 12 steps, my depression and anxiety problems went away. Stopped taking anti-depressants somewhere around the 9th step and haven't had a need for them in a number of years. When I straightened out spiritually, I also straightened out mentally, just like the book says. At the very least, you will be in a position to deal with any other issues when you recover.