You can put a serial number and G-XXXX registration on a double bed or canal boat should you wish
In the early 80s there was a craze amongst UK spotters for registering "bin-liners" which were basically model hot-air balloons - I'm not sure exactly how they were flown, if at all, though I believe one or two were radio-controlled. Tiring of this, the CAA gave them a special sequence (G-FYAA - FYZZ?). I'm not sure of the point of it and why the CAA allowed it. Odd thing is, some of those extraordinary R/C aeroplanes (did I see a pic of a quarter scale Beaufighter?) must almost qualify on size and weight alone!
One chap was so disgusted with the bin liner reggie practice that he registered a man-hole cover by way of a protest. Honestly, I'm sure I didn't dream this! I hope it wasn't in his back garden, or all the Reggie S Potters would have been breaking down the garden gate...