I have a set of Sony NC-10 noise cancelling phones that I use for flying and they reduce the sound of the engine but certainly do not eliminate it. They perform roughly the same as the Bose, which a friend let me borrow for comparison on a flight recently. I like the Sonys better, at 1/3 the price, since I have a personal aversion to that very processed Bose spatialized computed-sounding imaging, but hey, the Bose are comfortable and I suppose they sound pretty good despite all that. The Sonys are very uncomfortable, imo.
I don't think the issue with the noise cancelling circuit is risk of damage, I think the issue is fatigue. After listening to these phones, I notice a definite fatigue factor. My theory is that this is less fatigue overall, or at least a different and less bothersome fatigue, than the roar of 4 jet engines. But it's disconcerting and I don't use these phones when I have a choice.
Well, I can't say I love the sound of the phones, either the Sony's or the Bose. And I've read that the both will attenuate something like 10db ambient noise, compared with 23+db for well-sealed Etys in your ears that sound better anyway. Etys are in my future.
AM