Even if it has a serial number, I don't know if it would be register-able. When I got the KAL-C light, I called up CS to let them know the registration wasn't going through (it has a T and S number) and they told me those were not-register-able.
Ya, that's kind of a strange mash-up of qualifiers as the KAL C at $60 has both a serial number & a tool number, yet the LR 32 at $635 has neither. I also have batteries and a couple of chargers that don't have serial numbers and a Turbo Suction head that has a serial number but no tool number.
The KAL C can be added to the Festool Power Tools list but that's about it, any other information does not get displayed.