Welcome to the boards. I hope you like it here.
All the resorts I have stayed at (moderates and deluxe) have some beer, wine, and liquor at the resort, albeit at a premium price (I don't know about values). I don't know personally about the Beach Club, but I'm pretty sure there will be a place there to buy some.
Maybe somebody who has stayed there can tell us for sure.
Depending on how much time you want to spend shopping, and how much stuff you want to buy for the room, taking a taxi shopping to a supermarket / bottle shop nearby may save you money. But if you just want a few minor groceries or snacks and maybe a few bottles of something, it's probably not worth the cab fare or the investment in time.