Just chipped off a small part of my phone and small part of the screen, does AppleCare or AppleCare+ cover this?

Well, just the other day I accidentally dropped my newly replaced and naked iPhone 6 on pavement. So when I pick it up I noticed that part of the back of the phone was scratched and some of the metal was chipped off, even the corner of my screen was chipped off. However, I still have my AppleCare+ until October so should I try to replace it, or do you think I would be laughed at as it is minor and it is not affecting anything except cosmetics.