Do you mean an AppleCare+ incident, where you would get your Apple device replaced because of accidental damage?
You would have to ask that service shop about specifics, if you have a need for that support.
Yes, your AppleCare + would be accepted, as the shop, as an Apple Authorized Service Provider, would be operating under Apple's guidance and support. But, the privately owned shop may not necessarily provide support for all Apple products, and might be only authorized for the product that store can sell --- for example, any Mac, but no iPhones.
And, warranty service, with repair of a factory defect, should be covered -- assuming the shop supports that device, or that Mac. Some shops might not support iPhones, for example. Many do, but not all. They would refer you elsewhere, if that is the case.
Again, you would need to ask that shop about your specific needs. They are best able to explain their position in regards to Apple's warranty program -- and the support that they can offer you.