While you can change the app's icon image, these images must be saved in advance in the project directory.
Also, when the icon changes, the system will show an alert to the user saying 'You have changed the icon for {app name}".
Because of that alert, it wouldn't be possible to replicate what the Clock app does, since it would have to be A) done while the app is launched and B) would have to show the user the popup alert every time the icon changes, which in the case of the clock app, would be every second.