The ANC may play a part in this but there are vehicles that don't come equipped with it as far as I know. I flat out asked a GM engineer if my 2015 suburban LT had ANC was told it could (or not) but there was no easy way to tell without investigation of the radio and software installed.
A post awhile back indicated that perhaps the suspension was too stiff and what some are experiencing is vibration resonating up through the cabin. For my vehicle, I believe this is exactly what happened, and the key word is resonate. As an easy test (with or without a fuse pull or cotton balls) first find a section of road with a nice long row of raised center reflectors, usually spaced a few inches apart from one another. Driving safety comes first so you may want to do this when no other vehicles are around. Stop your vehicle and then slowly drive the driver's side tires over the reflectors, slowly increasing your speed to 5 -10 MPH. Maintain whatever speed you get to when the vibration starts, about 8 MPH from what I experienced.
The first thing you'll notice, at least I did, is that after a few seconds the interior of the cabin will shake and vibrate like there's an earthquake inside the vehicle, and the longer you drive the worse it gets. I am NOT exaggerating about the level of vibration here, it feels like the vehicle will shake apart. I would only drive with this shaking only for a number of seconds in fear that the vehicle would be damaged somehow. The second thing you'll notice is the pressure building up and the buffeting sensation reported here in this thread.
So, could it be the ANC contributing to this, I don't know, I'll defer to the acoustics experts here and at GM. What I do know is that I've never driven a vehicle that vibrated and shook like this before. I did the same test with other vehicles and yes, you feel bumps in the road, but the steadily increasing vibration and buffeting sensation, no. I drive on mainly smooth roads but I can only imagine the frustration by those with this issue AND with a long gravel driveway or daily drives on less than perfect pavement.
I ended up cutting my losses and trading out of this vehicle so as not to deal with the headaches, literally and figuratively. I wish you all the best and hope GM can come up with a fix as the new Suburban/Yukon/Escalade is a fantastic vehicle otherwise.