I've taken propranolol for many years to deal with public speaking. It works very well for that because your hands don't shake, your voice doesn't tremble, no matter how stressful the situation may be - it totally blocks the "fight or flight" response.
I can't say that it has had any effect on my alcohol cravings, or anxiety in general. I'm very doubtful that it would work for either. It's great for performers - actors, musicians, public speakers - but I've never noticed it made me need a drink less.