I have been reading (briefly, though), and it seems that the processor, at least in the Clara HD supports Bluetooth. It would require serious tweaks that go far beyond dropping a compressed file on the Kobo, but if the pins are accessible and we can find a compatible kernel driver, it should be possible in theory.
Edit: Here's the datasheet:
https://www.nxp.com/docs/en/data-sheet/IMX6SLLCEC.pdf