No, you cannot do this - the application has no say in this. Ask your boss whether he has ever seen a single example of an iOS application that would do this. There isn't ... not one I would bet.
The application can continue to execute some functionality in the background - streaming music, getting location information for example, but no application can block the home button. If you could do this, you could block an application from ever closing.
A) You couldn't technically do this and
B) Apple wouldn't allow it to be released on the App Store if that was the distribution route you were taking
If you look at the methods stubs created by XCode when you create an application delegate
-(void)applicationWillResignActive:(UIApplication *)application
-(void)applicationWillTerminate:(UIApplication *)application
That are filled will comments about how you can use this method to pause tasks, disable timers, throttle down frame rates, save data - there is nothing about being able to delay, query the user with an "Are you sure" message.
This whole idea is rather counter to the user-experience of the iPhone/Pad/Pod-Touch.
From the App Store guidelines (slightly abbreviated):
Apps that alter the behavior of switches on the device will be
rejected
This is a proposed change the behavior of the home button - so would be rejected.
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