Hi Audrey, I totally get where you are coming from. I don't really have any experience to share as the thoughts of leaving didn't happen until my AW had a major relapse.
If you were my daughter my advice would be you are allowed to put your own happiness first. Relationships are built on trust and I don't believe you trust him and I understand what it is like to be in a relationship where you are always waiting for the other shoe to drop. If you can find happiness with him then stay and if you can't then leave. It's not a decision you have to make now and to be honest it doesn't depend on his drinking or not drinking.
Your friend,