The receiver still requires that the input circuitry be tuned to the right frequency. Part of that is the antenna. If the antenna is the wrong length, it will reject the fundamental frequency. Trust me. WIth a degree in electronics, I'm not blowing smoke. Yes, it makes a difference.

Disconnect the antenna on your car and see what happens to the received radio station. Shorten it by half and see if you get the same quality of signal. It will receive, but the level of signal, and the range (very important here... ) will be detremental to operation.