No. It's the opposite: noise cancelling headphones typically reduce fatigue.
The opposing sound waves generated by active noise cancellation
technology end up blocking key parts of the sound spectrum (aka your
Not correct. The noise cancellation blocks outside sound, but doesn't not affect the spectrum of the music. Overall the transfer function from the input to the ear drum is very similar to that of a conventional headphone. The music is simply added to the cancellation signal and not affected by it.
With key parts of your music blocked, your ears are forced to work
harder to create sound.
Not correct. Healthy ears don't create sound. Key parts of the music are not blocked.
This creates ear fatigue and will leave your ears more fatigued than
standard headphones - this is why you'll never see musicians using
Not correct. I work with musicians and do listening professionally. Many musicians love noise cancelling head sets and use them all the time. Flying is pretty hard on the ears and noise cancelling headphones significantly reduce noise induced fatigue, to the point that I can work when I come off a plane. Which I can't without noise cancellation.
There is well established correlation between stress and noise levels https://en.wikipedia.org/wiki/Health_effects_from_noise and reduction of noise will result almost always in less stress, not more.
A side note: there are pathological conditions where the human ear actually does create sound. The inner ear has about 5000 neurons, about 20% of which are "efferent", i.e. they carry information from the brain to the inner ear. These information is used to actively tune a feedback loop that increases frequency sensitivity. Damage to these neurons or the associated hair cells can make this loop unstable and oscillation occurs which is measurable with a microphone. This is an extreme case of Tinnitus and the ears are quite literally "ringing". When working with a noise cancelling manufacturer, we found incidences where users reported significant improvement of their condition by using noise cancellation. However, that's anecdotal and as far as I know there is no solid scientific study to back this up.