Honestly if I was stuck with one of these shitty resistive heater stoves I'd definitely do this for stuff like warming up pancakes. Less energy and time wasted on heating the pan.
It's easy to clean, just use water and wipe it clear. Never soap. If you put soap on it, you'll ruin the coating and will have to re-season your stovetop again.
Well yes, technically the amount of heat released because of current going through the coil can heat things up on it's own, but this is generally a huge waste of power and kind of misses the whole "induction" part of "induction cooking". And those things (the coils) aren't meant to heat up for that exact reason. Edit: I really thought it was a shitty induction stove, but apparently it's just a resistive stove...