I know The Simpsons: Tapped Out game pushed users to their App Store page to update the app when necessary, so it is possible.
You should avoid breaking changes at all costs, especially without warning your current users. If you don't want to be able to support both users of the current app and users of the new version, then how about this:
Release an update to the version that's on the App Store now, that includes information about the changes, explaining that this version of the app won't function after X date.
Set your next version to be released at that date.
Don't ever put an option to exit your app in an app. It's an extremely poor user experience.
Topic:
App Store Distribution & Marketing
SubTopic:
General