However, my sister is an audiologist and pointed out something else- there really hasn't been a study of noise cancellation in loud environments, and it's benefit to ear health. While the cancellation is creating opposing waves and all, there's no study on the actual sound pressure that gets to the ear drum and possible effects of that, even if it is in an inaudible range.
With all due respect to your sister, active noise cancellation generates out of phase acoustic waves of equal amplitude to the incoming wave, and acoustically, the waves cancel out in the air, before they hit your ear drum. There is no energy left to hit your ear drum, and accordingly, no possible hearing damage (provided the phase is correct, which it is, because even with some temporal slop, they reduce most of the energy. Otherwise, they'd be amplifiers, and you'd know it right away).
More specifically, the generated waves are not in the inaudible range - i.e., they're not generating some infra- or ultra-sonic frequencies that do some sort of magic to your ears. Instead, they're the same exact incoming waves in the audible range, but with a negative amplitude. So, you get your loud wave at 100Hz and your loud negative-wave at 100Hz, and they cancel out to 0 amplitude, or 0 dB SPL. With no pressure, there's nothing to hear, and no possible way any energy could get transmitted to the delicate nerves in your ear. Accordingly, they can't cause any harm (unless, again, there's some delay such that that phase gets flipped back around, but again, you'd know it immediately).