Can AA help with depression? There is no absolute answer to this question. Some people find that it helps; others find that it does nothing; still others find that the program makes things worse. You can try it and see what you think, just remember that there is nothing wrong with you if you don't find it helpful.
Am I a dry drunk who can be restored to sanity by the steps? The term "dry drunk" is a pejorative term used by AA members to describe people who have quit drinking but are not members of that particular program. It is not a word that I use or an idea that I subscribe to. I will say this: if your depression was caused solely by the action of alcohol on your brain, then you will feel better when you quit drinking and to the extent that you find the steps helpful, they too will help you feel better. If, however, you have an organic mental illness, working the steps will not "restore you to sanity".
Have your mental health been helped by the program? Me personally? No. I found the "magic thinking" inherent in the program decidedly unhelpful. But that's just me; others do find it helpful.
The most important thing to keep in mind is this: do NOT refuse to take, or stop taking, prescribed psychiatric medications under the theory that "working steps" is the answer to mental illness. I cannot stress this enough.