You can assume it has a place, but not an critical one, since it is essentially unverified as to Army Standard. Any coach or teacher can administer the test, and everyone knows that many of those counting pushups and situps are probably very generous when it comes to giving credit for incomplete or bad form.
So what does that mean? It means the Application PFT is used to show you're not completely out of shape. It means that whatever score is on the application is taken with a grain, or even a lump, of salt. And it goes to the basic principle that information is only as good as its reliability, which in this case is not very high. The Army knows it can get a 180 APFT entering MSI to 280 within a couple of years, or even a year if they are serious and employ remedial training for any cadet under 280, as I've read one Battalion does.