No, the studio plus can not be guaranteed. It is the luck of the draw. Your 2 year old would be very uncomfortable in this so-called "day bed". This day bed is not anything like you would imagine a sleeping surface to be. Very hard, very small, very narrow - probably smaller than a crib. More like an upholstered luggage rack. It fits in the space where the door would be to a connecting one bedroom if the door existed. These are only found in the dedicated studio at BWV.
Your two year old would fit very nicely in the pack and play or you might be able to request a real crib when you arrive (they are limited).
The occupancy for a DVC studio is four plus one under the age of three. So as long as your two year old doesn't celebrate a birthday before your trip, you will be fine. If he/she does, you will need to get a two bedroom villa.