Its unlikely the a/c is causing this issue. It would not make a noise because the truck is turning. The problem you have is most likely the ABS cycling on because you are getting a bad signal from a bad wire harness at one of the front wheel speed sensors. What happens is the speed sensor drops out when turning because the wire harness going to the sensor moves when the front wheels turn and causes the speed sensor to drop out. The ABS computer sees this as a wheel that has stopped so it thinks the wheel has locked and cycles the ABS motor on. This will cause the brake pedal to vibrate or you will hear a short grinding type noise from the front end of the truck.
You need to have them check for any abs codes or check the wheel speed data when turning the truck at parking lot speeds. This is when this problem is most likely to happen, the speed sensor that drops out needs to be repaired. I normally replace the wheel hub and the harness at this hub. Your local dealership will stock the replacement harness. This replacement harness is not the complete harness but its a new connector to the sensor with about 2 feet of new wire that has to be spliced in to the old harness.
Let me know if you have any more questions on this issue.
I have not noticed the brake pedal shaking, and it is not really a grinding noise it is more of a moan.