Beach Club doesn't have different views as booking categories, so you'll be better able to cover all the options with waitlist requests there. (At other resorts, this isn't always the case. You're limited to 2 active waitlists, and there may be more than two room types/views that would work for you. In those cases, it's necessary to waitlist your top two choices, but also regularly check the web/MS to see if other options are available.) You don't indicate what size room you're looking for. If a two-bedroom, make sure you waitlist both the dedicated and lock-off options.
As the previous poster indicates, depending on when you're going in June, you may be beyond the timeframe of a waitlist. You can choose your waitlist search to end 30 days before check-in, or 7 days before check-in. There is no waitlist within 7 days of check-in. If you're that close, you'll need to be checking manually.
As to likelihood? That's anyone's guess. BCV is a smaller resort, so there are fewer rooms to go around. There's always hope with any waitlist, but once you get into the 30 day window the chances get lower. If someone cancels a reservation within the 30 day window, their points go into holding. People really try to avoid that. Emergencies and unforseen circumstances are a part of life, though, and bookings can still get cancelled at any time.
Have you made other plans for that night? Or will you just leave earlier if the night doesn't come through? I'm assuming you're not flying?
Another option if you can't get the room on points, is to see if it's available for cash. Cash and points inventories are completely separate. The fact that there isn't currently a room to book with points doesn't mean that there aren't any rooms available. If you book a cash room through
DVC Member Services, it can be linked with your points night under the same reservation, and you won't have to change rooms. Be sure to ask if the member discount is available. (There's limited availability for discounted rooms, and this close to check-in you may be out of luck.) The discount is 25% off the rack rate, if available.
If going with cash, you may be able to get a better rate if you can find a discount that applies to you, and book the room through Disney World's Central Reservation Office (CRO). The disadvantage of using CRO, though, is that you can't link that reservation to your DVC reservation. You will need to check out and check back in, and could very possibly be asked to change rooms.
