Background checks take place during casting on day 1. Your background must be clear before you attend traditions which is the third day, so it takes about 2 days. You will be notified if your background doesn't clear, which means you'll be sent home, theres also a situation where your background doesn't come back and traditions are usually postponed until they receive it. Also note that the only way you fail a background check is if you fail to tell them at casting about a prior offense like a felony or misdemeanor, traffic tickets you don't need to worry about.
Hope this helps you out
-Garrett