Quitting drinking didn'y cure depression and anxiety for me, it did take the constant withdrawal mood swings out of the picture tho. With each "come down" from the alcohol it was like the depression machinery got slammed into overdrive, absolutely horrific depressions while in alcohol withdrawal, couldn't deal with that any longer.
I gave up caffeine for a while and it seemed like my depression got worse without it so I went back to coffee. I guess with depression what works for one might not work for everyone. I know a couple of people who swear by giving up caffeine, I didn't get their great results so I guess the only thing one can do is try.