You are very wise to say you will not enter a covenant with doubt in your heart (I did with my ExH -- not an A but there were issues I pretended not to notice.) Divorce is ugly, and especially with an A from all the experiences I've read here.
Listen to your gut. Trust your instincts. If something doesn't feel right, explore that fully. If you think he's drinking too much now, know that this usually progresses -- he could drink even more in the future. I don't know your age/what stage you are in life, but if relevant. Would you trust the man he is today with a child's life? With your finances? Etc?