A few years ago, during a period of sobriety, I tried Wellbutrin (had no effect), Zoloft (made me feel very suicidal), Celexa (wanted to sleep all the time), Cymbalta (effects similar to Celexa), and Effexor (effects similar to Zoloft). In my experience, SSRI's, in general, made me feel really strange, like I was in a fog all the time.
So, to answer your question, none of the meds I tried helped with the alcohol or the depression problem. Over the years, I also took Naltrexone, Campral, and Antabuse to deal specifically with my alcoholism. Antabuse was a good deterrent, when I actually took it. It did nothing for the cravings, so I just quit taking it. The other 2 had no effect.
The only thing that has worked for me (aside from getting thrown from my car and breaking my neck) has been working the program of AA. I resisted it for 99% of my drinking career. So far, that 1% has made all the difference in the world!