I agree with the others than ordering an NA beer would probably lead to more comments than just ordering a soda or something like that. Also, I don't really have an opinion on the risks of NA beer, but I don't really get the point of it either. I didn't really drink beer for the taste, no matter what I said back in the day. Without the booze factor, I think it'd be a big, huge disappointment anyway.
About the date, I agree that you don't have to share the recovery thing on the first date. If it goes anywhere, though, you're going to have to share it pretty soon.