Actually, I've been told it's better for someone who gets a DUI to admit they have a problem and agree to go to AA. Don't have personal experience with it, but that's what I've been told. The grad school will also likely be more accepting if you own up to it and say you're doing something about it. Every person who's ever gotten a DUI says something along the lines of "I never do this, it was one time etc"
I'm not saying that's not the case for you, but I wouldn't try to explain it away. It won't be a deal breaker necessarily!