I dont think it will work...Not directly with LEDs. Radio waves inducted on an antenna are an alternating current, not a direct current, which LEDs expect.
You could do incandescent bulbs but not certain there's enough power to really light them up(depends on distance and directionality of the radio waves). I have seen people transmit with incandescent Christmas lights as an antenna, it works sorta, but that's a different power profile than receiving.
If you still want to do LEDs, you would have to find a way to convert the AC radio waves to DC... I don't think this is much unlike a strobe, so maybe you can modify one of those sound-based strobe devices to light the LEDs based on the incoming radio signal instead of based on incoming sound.