All heavy metal music sounds about the same to me. But I'm sure that is not the case for fans of heavy metal.
Sure, maybe they'd be better at picking out a bassoon in the mix than a metal fan, and a metal fan might be able to tell the difference between a Jackson guitar and a ESP guitar than the classical fan, but that's just due to familiarity, not their overall sense of hearing.
I don't think any serious musician would agree with you whether you're talking harmony or harmonics. However, listening to music in general will definitely allow you to hear different harmonic intervals better than if you didn't, but this is again just due to familiarity/ear training and doesn't overlap into your overall ability to hear.
We just use mnemonics. For example, Amen = 4th twinkle twinkle = 5th NBC = 6th etc.