ANR is more illusion than fact; while you don't hear or perceive vibrations or sounds so much in certain higher frequency ranges, assume that you're safe from hearing damage.
This is something I've been wondering about myself.
I have tried the Bose-X and for the audible spectrum they're great, damping most (but - I guess deliberately - not all) of the ambient noise. Communications are much clearer yet you can still hear some engine noise, stall warners and such.
But what about the inaudible spectrum? The Bose-X makes a lousy PNR headset so does it effectively filter out all the inaudible noises too? And is this filtering good enough to prevent hearing damage?
Or is a non-audible noise (frequency) not capable of destroying your hearing? (After all,
AFAIK hearing loss usually comes down to damage to the little hairs in the ear that are tuned to a specific frequency. Can they be damaged by sound of a different - possibly inaudible - frequency which doesn't bring them in resonance?)