Yes, the Diztronic will work with a screen protector. I have a glass screen protector on my 6P and the Diztronic works fine with it.

An alternative suggestion for a case would be the Spigen Rugged Armor. This is the one I use daily and it's basically the Diztronic with a bit more style on the back (the inlaid carbon fiber accents). This one also works perfectly fine with a screen protector.

Spigen Rugged Armor: http://www.amazon.com/gp/product/B016CBFBVI?psc=1&redirect=true&ref_=oh_aui_search_detailpage

This is the glass protector that I'm using: http://www.amazon.com/gp/product/B019O5MN4W?psc=1&redirect=true&ref_=oh_aui_search_detailpage