As someone who once bought fake airpods on ebay, I can tell you that Apple can't do this.

I spent a number of days with them where they were trying to work out if they were fake. The serial number was real but they were fairly sure the number had been taken from a real product and reused, but were unable to say for sure.

I ended up just returning them (because of the ebay return window) but found it interesting that Apple couldn't easily check this, and was very aware of the issue.