Hi NIG,
As you know nothing is ever simple. Basically the answer to your question is yes - BUT!
I have a thirty year old ITT FM broadcast band (89 - 108 Mhz) tranny which I tweaked to listen to my local App/radar freq. An FM set will "hear" AM transmissions. Inside are some adjustable capacitors on the tuning condenser. Twiddling these allowed me to listen to all sorts of 'stuff' in the seventies.
That's the good news.
The bad news is that, like most things in life, they don't build them like that any more. The chances are that the radio in your car is full of chips and uses PLL circuitry to generate its frequencies. This precludes the simply twiddling option.
Unless, of course, somebody out ther knows better.
(I think that hearing the tower tranmission when close by means that the signal is coming in through the IF stage in your car radio receiver. But that's harmonics theory and way, way beyond me.)