FM demodulation amplifier with saturation
The receiver's output does not depend on the input amplitude.  From the point of view of the receiver, the output only depends on the frequency/phase of the input.  

An fm signal in an ideal environment has a constant amplitude.  Another way of putting it is that fm modulation has a constant envelope.  Often this is advantageous because it allows the transmit amplifier to run at saturated output and not impact the modulation since amplitude is not varied as opposed to QAM and other non-constant envelope modulation types.  The same should hold true for the receiving side of the equation.  In practice I imagine you'd still need to watch out for overloading the receiver and causing harmonics and other nasties.

A write-up on my pyFmRadio blog post illustrates FM's amplitude independence from the modulating audio source.