For what it's worth, here's my experience. My wife and I applied (to different departments) at the same time. My wife got an offer, and then a contract, and I still hadn't even been contacted. So I called up and started asking some questions. Here's how it was explained to me.
Basically, if you check the "I'll take anything" box on your application, it goes to your first choice department first, where it stays for two weeks. If your first choice department doesn't "pick it up," it becomes available to all departments. But as soon as someone puts a hold on it, no other department can see it.
In my case (which may be unusual), the people in my first choice department (Rides) were apparently off doing job fairs and such the entire two weeks my application was with them. At which point, it became available to everyone and another department (Laundry) picked it up. In other words, my first choice department had never seen my application and now couldn't. It wasn't too hard to straighten out, though. (Basically, the person in Laundry not only took the hold off of my application, but then called Rides to let them know I was available. Which I thought was very nice.) It was smooth sailing after that. But if I hadn't called, I might be folding sheets at CP instead of checking lapbars.