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Yes, I have thought more about this, and I think that the signal would deteriorate. All the aerials within range and directional arc of the transmitter would receive the signal regardless of whether the attached reciever was turned on or tuned in to the particular broadcast. When the electromagnetic radio wave strikes the aerial it must impart some energy to the aerial or else the reciever would not know what it had to translate into audible sound, whether the top 40 or a tone or whatever. As energy cannot be created or destroyed, each time the wave strikes an aerial then an amount of energy must be lost to the aerial and it would eventually run out.
I think, therefore, that recievers behind all the other aerials, listening or not, would possibly eventually have too weak a signal to convert. Of course, the signal would also be absorbed by and bounced off other surfaces to further add to its reduced energy, therefore making the effect of the other receiving aerials difficult to actually measure.
I don't know about crystal radios, but if they have no other power, then yes, they must be sourcing the energy from the radio wave.