ANR headsets are powered; one can't draw enough power from the audio signal.
I agree the whistling is most likely a feedback issue with the noise cancellation circuit (which uses a mike inside the earcup, wired to achieve a null sound level pressure inside the earcup with zero audio signal) but
It would be very surprising if the input impedance of the headphone changed significantly when the active circuit is turned on. So I think this is more unlikely.
this is still possible because e.g. presenting an excessively capacitive load to a badly designed audio amp could make it go unstable.
But, as I've said before, I think the 17-79 is a crap headset in terms of performance.