Happy to give my insight! It honestly depends on the resort and can even vary from day to day within a certain resort. Those resorts that focus on groups (ie: CSR, Cont, All-Star, etc.) my begin blocking their rooms as early as 5 days out or more to ensure that groups are blocked together, etc. Those that do not, may wait until the day before or even the day of to assign a guest a room. Additionally, if any resort is close to or completely full, they will usually block each room to ensure that everyone has a place to sleep at night without being forced to move rooms halfway through their stay. It's really like a giant game of Tetris everyday.
On too of that, because Disney hasasenit a priority to give guest clean rooms when they check in, whatever the time, rooms may be move around by the operations team to try and get a clean room upon arrival. Of course it's not always guaranteed but they will do their best.
This is why online checkin is so beneficial to that process. When you tell us when you're going to be here, we can more accurately plan to get you a clean room that meets your requests as fast as possible. Of course it's not always available but it certainly helps.
In light of all that knowledge, I would fax your request over to the resort and also call whoever you booked with to have it added to your reservation.
Sorry for the novel but it hope it helps!!