There are some SSP guys who have been sitting in the pool for 9 months and still haven't received the clear to train.
I had lunch with Arnie a few months ago and asked him about this very thing, he just kinda rolled his eyes and said, Delta has no control over when first advantage (the background check company) gets them the info back. However if its been more than a few weeks and you haven't heard anything, then you are good.
I know a few guys who were contacted by first advantages because of some discrepancies on their application, and they were contacted about three days after receiving their CJOs. So I wouldn't sweat it Beezer.