If you have already made a downpayment, you are most likely already in the DVC system and can make reservations using the Developer points you have received. You do not need to have closed on the contract to use the DVC membership. You won't receive all of the documents until after closing.
As Doc said, if you give them they downpayment you are pretty much there We actually used some of our dev points while we were there in November. Literally less then 2 hours after we signed and gave them the deposit, we were packing up at CSR and heading to SSR for the last 3 nights of our stay Had our cards handed to us that day.
Congratulations on your purchase, WeLoveAriel0505!
Here's our time line:
11/20 - Purchased 283 points @ BLT while onboard the Disney Magic
11/26 - Called Member Services and booked a cruise using our Developer Points
12/5 - Called guide with final payment information
12/19 - Received call from guide saying we had closed
12/22 - Received DVC Member Cards