The active noise control can't be deactivated unless you yank the subwoofer's connections, remove the amp that goes to it or rip the audio system out (and you'll likely lose the HVAC controls if you do that). My wife has a 'Nox, active noise cancellation is fixed. It's interlinked with the audio system and subwoofer in the rear. Don't mess with it; if you do, you'll dislike the result. I don't know if the mic being deactivated/cut will do what you want; the result will be an open loop amplifier (don't know what this system will do) and a check vehicle warning in the dash.
We had it once, and only once, for some reason deactivate for about 10 minutes. The interior was BOOMY loud, a really 'thrum' like uncomfortable boom, typical for a large displacement 4 banger. After the car was cut off and restarted it never, ever did that again (been 19 months since it happened). It was a lesson in how well the active noise cancellation really works and why the Equinox can be so quiet inside at lower RPMs. Most 4 bangers aren't this quiet at low RPM.
And why the audio controls interlinked to the HVAC? The two seem to be interlinked based on a TSB from a while back (early Equinox/Terrain models had a defroster issue that was fixed by reprogramming the HVAC module). Audio systems in the 'Nox can be actively controlled by OnStar (fan turned down and audio system muted when announcements are made), hence the HVAC and audio systems seem to be interconnected.
Just leave the system alone.