> I am very interested in how iOS/OS X handles application
> updates through the app store.
On iOS, if you install an update to an app from the store, then any currently-running instance of the app is killed first.
Only one app is "foreground" at any time on iOS, so when the App Store app is in the foreground, the app being upgraded cannot be. When an app is backgrounded, it is told that it is going in to the background and it is expected to save its state. It might eventually be resumed but it could be terminated without any further notice due to power-off, low memory, etc. So the case of an update is not special.
I don't know how it works on the Mac, where presumably the app being upgraded might still have windows visible. My guess is that it is killed with some notice first.