OY! FM is frequency modulation ... the error signal in a PLL is used to change the VCO to "match" the carrier frequency ... In other words the the error signal IS the demoulated audio if you are talking mono... stereo obviously requires an addition step
You don't track the modulation in the tuning, you do the de-modulation after it's been amplified down the IF, if you could track the tuning modulation almost none of the radio stages would be required.