Microwaves cook because water absorbs the energy, because water resonates at the frequency of microwaves. All sorts of molecules in the body resonate at different frequencies. Just because the nerves in your ear don't register warmth doesn't mean that other molecules in your body aren't absorbing energy. The body has few sensory nerves below the skin anyway.
The amount of energy is much smaller, yes, but it is also quite concentrated. I'm not saying there is an effect, I just don't know, but it is possible and it is definitely worth studying.
Especially around lots of mitosis, I would imagine.