I was on Klonopin for 2 1/2 years and it helped me stay away from booze for about two weeks but I eventually fell back into it. And was drinking on top of the benzos which led to scary blackouts where I did insane **** I don't remember.
Remember, benzos affect the same receptors in the brain that alcohol does, GABA. So maybe it'll help you stop drinking but benzos can be just as addictive and habit-forming. You might just end up trading one addiction for the other.
Everybody's different though. I would just say tread lightly and don't fool yourself into staying sick.
Maybe some of your anxiety is coming from the alcoholism itself?
Either way, hope it works out for you.