There is a common understanding that active-noise-cancelling headphones protect your hearing because they reduce outside noise and allow you to listen on the headphones at a lower level but they do not directly address the question of hearing loss.
For example in the article How noise-cancelling headphones help to protect your ears published on the "Western Hearing Service" website. They talk about the ability to listen at lower volume but no direct studies on hearing over time. E.g.
A study published in the Ear and Hearing journal found that listening to music with headphones at 70 per cent volume for just an hour can bring you to the threshold of your safe listening limit. By using noise-cancelling headphones that enable you to enjoy your favourite music at a lower volume, you are able to listen safely (60 per cent volume or lower) for longer without the risk of hearing damage.
Although there is a common understanding that they do protect hearing through lowering the level of noise required to hear what you want to listen do, have they been directly evaluated for their ability to protect hearing.