I sent everything to AADSAS, including letters of rec., in mid-may last year. The AADSAS number that is assigned to you is given in the order your app. is received. I was somewhere in the low teens and I was invited to 4 schools for interviews BEFORE taking my DATs...and no, my GPA wasn't great. I just happened to be in the pile of applications that are sent very early--first interview cycle. They also take their time in processing your application so you don't want to wait until they have a ton of apps to process.
I'd recommend sending the stuff in ASAP, even if you're DAT isn't scheduled until Sept.