I had lunch with some real technical and physics wizards today and got some answers.
They knew of a case of a farmer who strung long lengths of barbed wire underneath high tension lines and got significant power off them, and when caught went to jail. It's stealing and loads the system.
I also asked about florescent tubes glowing beneath the power lines. They also load the system, but, depending on angle, can load it magnetically or electrically (like a transformer or a capacitor). In either case, it loads the system and is stealing.
At a distance, however, the wavelength complicates things. A coil that, for example, is beside a power company transformer that charges a battery, produces a "back EMF" that radiates back into the power company's transformer, reducing the power in the transformer and in the electrical grid.
With a radio transmitter, a receiver would load the transmitting antenna if it were less than one wavelength apart. The receiver would then transmit an opposing signal that would eventually arrive back at the transmitter, and its effect would depend on the phase relationship. The transmitter may even be turned off by the time the back EMF arrived, as pointed out above, making the transmitter, briefly, a receiving antenna for the incredibly feeble (by this time) reflection.