In the video I linked to the guy is lighting a blue LED and he says he is getting around 3 volts at 3 ma or better. He also mentions that he is a mile or two away from the station transmitter as well.
I did a quick online search and it's a 10 KW daytime station transmitting on 1270 AM from Grants Pass Oregon.
I am not sure what you consider decent power but I know of a lot of electronic circuits and devices that would find 9+ milliwatts more than sufficient.
Use that to charge capacitors or small batteries and you have a lot more short term power to work with as well.
To me the whole concept seems very doable in the right circumstances!