It's not possible GSX would affect the yaw dumper, surely not in normal use. While GSX is pushing, the airplane is frozen, so it's normal something might not work, but this would only happen during the actual pushback movement.
In every other situation, GSX doesn't change anything on the airplane, not even during refueling, since the PMDG737 is internally flagged as having a custom fuel system, so it's never actually refueled.