Can a current transformer drive a low-power FM transmitter?

I'd like to know if the dryer in my apartment complex is being used. My idea is to have a current transformer drive an AM or FM transmitter, very low-power, to be able to remotely listen to when the dryer is in use. The current from the dryer would ideally cause the transmitter to turn on when in use and off otherwise. I would have no problem getting a current transformer around the supply lines to the dryers and low-power fm transmitters are pretty cheap. I'm specifically looking at transformers by CR Magnetics. They can supply the voltage required, which would obviously need to be rectified and smoothed, but could it drive the needed current? And if this all works, what would be a good way to generate a tone to transmit over the air (also driven by the transformer)?

Electrical shops (and many supermarkets) sell mains power monitors, intended to enable consumers to observe their power usage.

They commonly have a wireless transmitter on the unit that fits around the supply cable, and a remote receiver unit that displays the power being used.

I think one of these kits will serve your purpose. (Unless you are very keen to invent your own !)