beccart's journey

I recently interviewed for a teaching position at a local school, and honestly, I thought I did poorly during the interview. To my surprise, a few days later, they asked for my references, which I provided. Shortly after that, they sent me some exercises to complete, and then I received a request for a background check. This is a bit unusual for me, as I’m used to background checks being conducted only after a job offer is made. I'm now wondering if I should follow up with them after the background check is completed. Is that considered appropriate? I appreciate any advice!