I believe that noise-cancelling headphones have a problem in the VR context. Due to their nature, they play a sound that counteracts the sound you do not want to hear. It’s highly likely that this would affect the fidelity of the sounds generated by the headset for the experience you are having (despite this being from a direct source).
VR sound (AKA Binaural or HRTF sound) often relies on some very specific frequencies that allow us to perceive the direction from ‘reflections’ that are very subtle and sometimes barely audible. I’m not saying it would deliberately remove sounds from the channel being played from the VR device, but the cancellation waves would have to have some effect on the sounds coming from within the experience.
If we allowed an algorithm to indirectly dismiss some sounds as background noise, they would quite likely remove some of this important information and reduce the overall immersion that is so important to the VR experience.
If the algorithm could be expanded to specifically avoid frequencies that are being generated for the experience, then that may produce a higher fidelity experience. Were that the case, then the external noise-cancellation would also be necessarily be reduced by that same algorithm. The combination of the ‘allowed’ internal/external frequencies would mean some sounds would be unintentionally amplified (by virtue of the fact other sounds were comparatively cancelled). This would hinder the brains ability to make sense of the sources/directionality. I don’t think it would be a major effect, but I would estimate that it wasn’t negligible.
So, the net effect may be that there isn’t much difference between noise-cancellation and normal headphones or that the noise-cancellation may inhibit the immersive quality of the sound field. In which case, you’d have to wonder what was the point?