Yes. Because the differential is part of the drivetrain that delivers power to the wheels while allowing them to rotate at different speeds, problems can affect how the vehicle feels and sounds while driving. Depending on the problem, you may notice noise, vibration, clunking or changes during acceleration, deceleration or turning.
Those symptoms can also originate elsewhere in the drivetrain. Certified Transmission in Bellevue can evaluate the vehicle and determine whether the differential is actually responsible.