Short answer: Yes, you can get beer at the Screen Door in BWV. Cost is lower than in USVI (which is not suprising as just about everywhere is cheaper than in USVI), but more than at the local megamart or upstate. It's not outrageously expensive, and there is a modest but decent selection of brands; the price differential is made up for by the convenience of being able to buy it right there.
If you want a better price, but a bit of a schlep (at least with heavy beer crates) there is a Hess gas station/ kwiky-mart type place behind the Boardwalk where things might be a little cheaper. But you'd still have to carry it all back to the room afterward.
Good luck!