If your disability claim has been denied, you should expect to receive a denial notice almost immediately. If it has been approved, you should expect an award letter within a few days unless there are mitigating factors.
It took mine 1-2 months back in 02. With all the vets returning, I expect it could take even longer than that now. But, if it does you will receive all the money from the date you were rated, so no loss there.