I believe it's a full sleeper, bit you could call MS to be certain. All of the studios we've stayed in (except OKW, of course) have had a full sleeper.
The accommodations page on the public DVC website lists it as a double size sleeper sofa:
Studio (sleeps up to 4) 355 sq. ft.
Kitchenette with microwave, mini-refrigerator, wet bar and coffee maker
Queen-size bed Double-size sleeper sofa
TV
Private porch or balcony
It's interesting that they don't use the same content for both the member's website and the public one. Multiple copies of the same information is not a good thing and it appears they have trouble keeping them in sync!
I stayed at SSR in a studio this summer and was on a full sleeper sofa...they are a new type of sleeper sofa where it is in 3 parts and when you pull it out the parts come together...so you don't even know you are on a sleeper sofa...maybe all of Disney is like this but I had never seen one before...it was incredibly comfortable and I didn't even know it wasn't a "bed" It does cramp the room up but worth it if you are on a budget...