The app will not preload every time new items come in. This is a common misconception about iOS 7. iOS 7 schedules these apps to run very infrequently to save battery. Some times it will take many hours to do a background refresh.
I've got a few apps built using this API, so I can chime in. It is definitely based on usage patterns--the more you use a particular app, the more often it will refresh. It's also certainly based on battery life at the time, but also the requirements of the app.
With Pivit, since it's such a compact fetch, it'll happen more frequently than if you were, for instance, downloading photos. I check HN a lot, so for me, the app is always up to date. It does take a bit of learning time for the OS to know your patterns, but it is well worth it--it's really a great new API.
It seems to be smartly batched with other network fetches. I did some tests using a local notification to let me know when it occurred, and it happened most often when sending an app into the background or finishing up another network task.