Heated flooring under subfloor
I had an embedded electric floor heater in my basement on concrete.  The builder put it in to "take the edge off" and then put laminate flooring over the subfloor with the heating.  What I think might be relevant to your situation was that the heat felt quite different than it did in the washroom where they used tile.  It still made the room warmer overall but it took much longer to warm up and the floor itself never felt as warm as the tile did.

I think what you'll find is that the heat will transfer up into your washroom, but it won't be as warm/efficient as it would be if it were embedded in your tile.  If the heat doesn't transfer well, what might happen is the thermostat you have to install might never reach temperature to shut off.  In which case you'd just have to turn it on and off when you needed it and maybe plan a bit ahead, which is what we ultimately did with ours in our kids room at night(bedrooms were in the lower level).