We've been tasked with fading the screen when a menu item has been clicked and JQuery is the way forward!
In the below instance the class 'fading-menu' was added to the WordPress menu items that needed the fade effect (via 'Appearance' > ' Menus' (after showing classes via the screen options on the top right)).
We didn't just link any and all menu items as one URL is to a download file, no use in fading the screen for that!
This method does have its flaws, clicking the back button on your browser may result in returning to a faded out screen.
Enhancements to follow?