Control: tags -1 - moreinfo I still don't know any examples of an unpaired bluetooth device triggering dmesg entries at boot time. (If this ever happens with any such device, I would be interested in knowing how and why.)
But since you asked, I tried it anyway. The device enters pairing mode as soon as I press the wake button, and goes back to sleep if not paired after several seconds, so I had to carefully synchronize it with choosing a boot entry in GRUB. As expected, dmesg | grep -E '( bt)|bluetooth' yielded nothing interesting. So btusb (the module affected by 2c1dda2acc41) was apparently not complaining.

