Yes, it would be covered.
However, I would recommend you get this fixed through Apple instead, especially if Total Care determines it is damage and not a manufacturer defect. If you go through Asurion and they determine it is damage, you will have a $199 copay to get a used replacement phone. If you go to Apple, iPhone 6 screen repair is only $109.
Well, Verizon said it was damage, even though this thing has never been outside of a rugged case, was never in a pocket or anywhere else that would cause the phone to flex or separate. It was obvious that the adhesive failed, yet they blamed us. Good going Verizon.