Depends. On big jets, or rear engined jets, the engines are so far back you might not hear mechanical noises. Modern jets have sophisticated warnings, ECAM or EICAS, for all systems.
I was wearing Sennheiser HMEC active noise cancelling headset and could hear banging on (medium size) A321, which sounded like an engine stalling, but was the #1 electrical generator loading and unloading owing to a dry joint. But the cockpit was lighting up like a Christmas tree with warnings, so we wouldn't have missed the problem had we not heard it.
Noise is very fatiguing, and will cause hearing loss, (which cannot be cured), so it is more important to protect hearing in my opinion and essential on long days. Small GA and piston aircraft without extensive system monitoring perhaps need the mark one ear listening out, but such aircraft don't tend to fly 8-10 hour sectors!