At least you are supposed to be allowed to transmit on AM (and FM) bands at very low power, at least under FCC rules. That's how they can sell those adapters for car radios. Some other ones you definitely are not supposed to use as far as I know, like the old analog TV signals - I've seen a couple of those sorts of projects recently. On the other hand, you can go and buy an illegal TV transmitter on Amazon right now.

Also a reasonably even bet that you already own a low-quality wall power supply that will produce more interference than anything you're going to be doing with a Pico and a 4" jumper wire (I've found a couple of offending devices in my house), but I'm certainly in no position to tell you if you should or shouldn't do something.