Now you have to keep in mind that his car experiment took place during the later portion of his coil days. I believe that he used his Canadian tower(Magnifying transmitter) as the transmitter for all the power he received. I also don't believe the story is accurate in its details, especially time. He more then likely did use the '31 Pierce Arrow, but not during 1931. To many details don't add up about that car when the eye witness reports are mentioned.
Although what I have read about Tesla's coil transformer system, leads me to believe that the every day coils were just a starting point. The Wardenclyffe tower was the finished product which used a third coil(
helical resonator or
cavity resonator) as the transmission coil.