Firstly, be more careful about what you're talking. You don't add subviews to viewcontrollers, you add subview to views, i.e (self
is a view controller)
[self.view addSubView:myView];
Also, you don't push views, but viewcontrollers, i.e
[self.navigationController pushViewController:otherViewController animated:YES];
Now with the first statement above, the view has a new subview. If you push a new view via navigationcontroller (second statement) over the original view, this does not really affect the original view. So, the subview you added will still be there after you pop the new view(controller).
See it like that: Your first view controller has a view called View1. You added a subview to View1, fine. Now a push using UINavigationController pushes a new view controller over your old view controller, so you now see its view, View2. This has nothing to do with View1.
To answer your second question, see Add same subview multiple times to view
Short answer, the view would be deleted from and instantly inserted into the parent view. So, while pointless, nothing bad would happen (the subview would just be pushed to the front).