You asked if he could get custody. It depends on your jurisdiction. Most state laws don't provide any protection to kids of alcoholics. The law assumes a child needs both parents and doesn't recognize that alcoholism is a progressive disease that just gets worse when the alcoholic won't work on recovery.
That is certainly the case with my state. It took me a long time to decide to split, and I stayed out of pure fear of a small child being left alone with an alcoholic. The courts in my area will give maybe a 30 day supervised visitation, require the alcoholic to have AA check a box for those 30 days, maybe visit an outpatient center, etc. You might get an injunction against the alcoholic drinking around the child or some form of testing that mostly requires the sober parent to continually monitor the alcoholic.
Personally, I wish courts would order an MRI and see the shrunken brain. Then, if the alcoholic gets off the hooch and sobers up and regains their brain and the better judgment that goes with sobriety, THEN they could get shared custody. It just isn't fair to kids to subject them to unpredictable, ranting, screaming, night-peeing alcoholics.
Separation and divorce has given me so much peace and lowered my anxiety considerably. Our child is doing better as well - on the whole. He has one stable home where there is consistency, love, discipline. On the dad-every-other-weekends, there are some good days with museum trips and Lego building, and there are some awful days.
My biggest fear is the harm from unsupervised visits when my ex is drunk - for example, a friend told me (a day late) that my ex was drunk when he drove my child last week. How do I protect my child?