You would be able to tell if the user had previously used the app, gotten to a state, switched out, then went back to the app to find that state or if the application was pushed to a certain state when it was opened.

Personally though, I would prefer the back button system-wide only. You can easily provide a UI element to take you to the top of the stack (especially since when an app is forced into a state, you only want to get to the top of the stack). Sometimes I even get confused when the back button takes me back a webpage in the browser.