Yeah, pretty sure it links to your PC or console through local wifi or bluetooth and connects real-time to the game. I don't think you'll be able to do anything with the app when you're not in-game. (At most you might be able to see the state of your Pipboy when you last exited the game.)
Other games second screen apps have used WiFi and were real time. I rememeber when X1 first came out and a buddy and I were playing Battlefield. I was using the second screen as the "commander" and he was fighting. It all worked in real time to do stuff I was doing on the second screen. Bombing here and there, sending people to one spot, tagging snipers
Some are thinking the pip boy useage is also done in real time like a lot of other mechanics now are. If that's the case it may be feasible to have the app up to switch items/ heal during a fight
Would be cool to have the app always displaying the map so you could quickly glance at it, and use the ingame Pipboy for everything else.
I was under the impression it works real time with the game, so you can use the pipboy on your wrist to use the pipboy in the game.