No, you should be fine. Only a handful of schools send background checks if you are waitlisted. For a school, sending a background check without a waitlist or acceptance decision is very unlikely.
Assuming you didn't hear back from the school this morning, when I was given that notification from Certiphi pre-II decision, it said it was sent because the school had reached a decision of either waitlist or conditional acceptance. I found out a few days later regarding the school's decision. I don't know if you want to complete it before, but it seems like good news!