I think abuse is probably more common among people with addictions than in the general population, but I worked for nine years in the DV field and tallulah is right--not all alcoholics are abusive and not all abusers are addicts. The most sadistic abuser I ever encountered in my career didn't touch a drop of booze nor drugs, and the worst psychiatric disorder ever diagnosed (according to him) was OCD.
I think alcohol magnifies abusive tendencies, and even those who would not be overtly abusive sober can become so under the influence.
But active alcoholism will make ANYONE poor relationship material. For a number of reasons, including dishonesty (not necessarily stealing or cheating but simply being dishonest to protect the addiction), manipulative (ditto), "emotionally checked out" (good way of putting it!), unreliable, etc.