We applied with US passports late last Friday evening and my wife's application was approved almost instantly. My application did not get approved until 8:30 Monday morning. It might have been a typo but otherwise the main difference is that I also have a UK passport. Whatever it was didn't take long to get fixed when they re-opened but it is a warning that if you really need to have the approval it would be wise to apply during office hours. As long as they only require you to have applied it doesn't matter.
The desktop process worked very well and didn't take long. Taking a photo that I liked and getting a passport scan with at least 200 dpi resolution took the most time.