Normally, if you purchased it from Apple, that’s not necessary and wouldn’t work anyway. When the serial number is added the AppleCare software would just pop up an invalid device or coverage not available, some wording like that. When I had my Time Capsule swapped out it was because my AppleCare for my laptop was still in effect. But I had purchased the Time Capsule from Apple so they already had a record of it. I’m not sure how this works when buying from a 3rd party. Having a receipt should be sufficient. But calling in to speak to someone is a good idea, I’m just skeptical that there is any mechanism to add a device that is not covered by AppleCare. Best Buy should have its own coverage available.