Erm... not quite in the same sense IMHO, we're still putting the kettle on to boil. When I flick the switch, the kettle is 'on'. It's even in the 'on' position :)
I'm not sure the etymology of "put the kettle on" has been strictly about a stove-top for a very long time. To me it's a method-independent phrase, and a reference to setting the kettle to boil, not its physical placement.
When cast-iron stoves were common and possibly the primary source of heat for many homes, I am pretty sure that for most of the cold parts of the year, they would be fired-up and kept hot most of the day and night for warmth.
So - it wasn't a big production to boil water, you would just put it on the already hot stove.
(And also - I did not know this until recently but kettle can mean just a large cauldron/pot - although typically it would also have a wire handle and a lip/spout for easy pouring. Hmmm they were also used to hang above campfires, so my stove theory might go even further back...)
Ah, that makes sense! I guess I was assuming that "on" was in reference to it's placement _on_ the stove. But turning the circuit _on_ makes sense too.
