I'm not really sure why you would want to pass a different model to the UITabBarController. The only thing tab bar controllers do really well is managing the tab bar. Their "model" is basically a list of ViewControllers which they then present to the user if he taps a tab bar icon.
In the documentation Apple says the UITabBarController class is not intended for subclassing, but you could still do this if it were neccessary.
But if you just want to do this because you have convenient access to the tab bar controller from within your other view controllers, then I'd recommend leaving the tab bar controller allone and implementing some sort of a NoteManager class (probably as a singleton) and simply using it from your other view controllers.