I went to my first semi-dry wedding a couple of weeks ago. The bride doesn't drink, although the groom does. The bride's parents don't drink, but her brother and sister do.
Whereas usually there'd be wine on the tables, there was only fruit juice, water and sparkling soft drinks. There was no bar available. However, when the meal finished at around 7pm, they opened the pay bar, so guests could buy their own drinks. FI and I are both quite big social drinkers and do enjoy a few drinks at a wedding (it's the only way I can get up and dance!). We were on a table where we didn't really know any of the others and I think we took longer to loosen up than we otherwise would have done. There was a lot of hanging around when the bridal party were taking photos and we just had to stand there and wait. Had we been able to have a drink, it would have at least passed the time (I have to clarify here that there were no soft drinks available either, just standing around!).
I think you'll find it hard to control in an AI resort. There's no reason why you need to have wine on the tables, but I don't think you'll be able to stop people going out and getting their own drinks.
Good luck and I hope it works out for you.