Hello HopingforCure,
Welcome to SR! I am sorry for what brings you here, but very glad you have found us. You will find a great deal of support here...for you!
Although I know this is not what you want to hear, but no, I would not marry the alcoholic you are describing. If he had a solid recovery program and had been sober for a number of years without any slips...if he was humble, transparent in all his activities, and was rigorously honest about his current and past situation, then maybe yes.
This is a decision you have to make for yourself. I hope before you do, you will take some time and educate yourself more about the disease that is alcoholism. If your boyfriend decides for himself that he wants to be sober, that's great! But right now he is just at the very beginning of a lifetime of work.
Sending many hugs and prayers as you struggle to make the best decision for yourself.