It is not. Serial numbers are per device. In fact even the parts have independant serial numbers so any add-ons like trays and finishers have their own as well.
That said, when you call Xerox they just want the one for the device you are calling on. And if you call on the wrong one you are likely to go to the wrong group. Due to the vast array of products employees cannot be expected to know the ins and outs of all products from a small Phaser to a Full-on iGen.
There are scenarios where a copier has an external RIP, like a Fiery, Freelfow, Splash or Creo. In most cases they will want the Serial number that goes to the copier portion, but if going to 2nd level support you may be asked for the RIP serial number. Typically not though.
No 2 devices have the same serial number, but 2 devices that are attached together physically can be identified by the one on the largest piece.