No. The mechanism is destructive interference (and not destructive to the eardrum). The undesired frequencies (ie. Non vocal) are sampled by a small microphone within the ear cup and a wave of completely opposite amplitude is broadcast to cancel the original signal out. The net result is NO sound at the attenuated frequency (theoretically). How can that possibly affect your hearing? It can't.
The only ANR that might possibly be harmful are those fitted ear plugs (which are, by the way, almost weightless and work very well) that could allow bacteria and moisture to build up withon the ear canal.