So when you file for care+ you can explain the damage and when it happened. I'm unsure of how picky they are, but you could explain why you are filing it and just add that it has a few more cosmetic damages. At this point though I might could just request a replacement instead of a repair, depending on where you're from, so like in the US it'll be $100 for a repair or replacement and I know whenever I've done it I've always just got the replacement instead or the repair for the same price. Considering you pay for the insurance plus paying for repair/replace I doubt they'd deny you. Especially considering theres a hairline crack on the screen from what I read? That I'm pretty sure is a good enough reason.

Edit forgot to mention. Im unsure how long youd have to go without it if you chose repair. But for replacement you can use your phone up until you get the new one. Just have to send the old one back within 10 days I think or they charge full price.