Can a relationship with an alcoholic in it really work?

I’ve been dating this guy for a couple of months and noticed since day one the alcohol excess. I had never been with someone like that so couldn’t really know if it could work or not. He’s a sweetheart but he also is inconsistent and rude at times. I don’t know if its all due to his alcohol or not but just in case I did mention it to him. I was kind of negative about it and ended up breaking up the relationship. He agrees that he drinks too much but said our problems wore mostly because of my trust or issues from past relationships (it sounded like an excuse). So the thing is that I do miss him and I’m thinking about giving it another try but I’m also scared that it might be a big mistake. Any advise could help. Specially those that have been in alcoholic relationships in the past.