Is this wait time normal for mortgage approval?

I applied for a mortgage through USAA about two months ago and was pre-approved. After I found a house I signed a contract and my application became conditionally approved based on several items I had to send in to verify income, credit inquiries, debt, etc. I sent in all of my paperwork and signed all the necessary documents about three weeks ago but my online loan status still says all of my tasks are still pending. On that same page it states that all paperwork and documents will be reviewed within three business days. I called USAA to confirm that they received all my paperwork and they said they received my documents but they had not gone through them yet and probably wouldn't until a few days before closing. Is this normal? Should I be worried that I could still be denied even though I am supposed to close in a week? It just seems like it would make sense to review the paperwork early so if there were any discrepancies they could be fixed before closing.