The headphones work with a cable - without you having to switch them on. Simply by plugging in the cable. However, the noise cancelling will not work because all the electronics with the microphones need to be switched on to analyse and filter the ambient noise. If the headphones are switched on, the NC will also work.

Yes, of course, tested on a flight lasting over 12 hours. Connected by cable, in ON mode, the battery didn't discharge and the noise reduction worked well. Perfect for listening to films or music on the plane and during the journey.

I can confirm that the ANC works by switching on...

I'm not sure, but I think it works.