They have a "zero tolerance" policy regarding alcohol consumption, but I've never seen any indication that they enforce it. Although you are only going 25mph, being broadsided by another kart really, really hurts, so hopefully they don't let people race that are visibly impaired. (I'm sure their insurance company won't let them)
I really hope this is granted. Often the wait time is over an hour and it'd be nice to have a beer while you wait. Also, often people go just to take family members and watch, so there is no reason they shouldn't be able to have a drink.
I'm really glad this place is doing well, it's really fun and a great thing to do with friends on a rainy night.