In my wood stove, at least, it would drip though into the ash catch, which is a much thinner metal than the cast iron stove body and not really meant to have something actively burning in it. Kerosene also likely burns hotter than wood.
So you’d have a too hot fire burning in all the wrong places in the stove, it might be ok and it might burn a hole through something and start a fire.
People have actually become more unhinged: https://www.iata.org/en/pressroom/2023-releases/2023-06-04-02/