Do existing large commecial jets make use of differential thrust to control yaw?
No, differential thrust is used in normal operations only when maneuvering on the ground, and then manually, not driven by a computerized control system.

It is preferable to run all engines at the same speed. Not only would you add additional frequencies, but also the beat frequency between pairs of two engines if speeds differ. This makes it harder to check with your ear that all engines are humming away nicely and generally creates more noise than when the engines run in sync. The answers to this question explain what the beat frequency is and how synchronization is achieved.

Next, the lag in engine response makes the control loop prone to oscillations. A rudder command is executed quickly and precisely, and when the deflections are below maybe 10°, no profile drag penalty is incurred. Induced drag due to lateral trim should be very small, especially at high speed. Trim deflections are normally much below that value, so an efficiency benefit from trimming with differential engine speeds is unlikely.

During take-off and initial climb both engines run at maximum thrust, and any trim requirement would reduce total thrust. This reduction is small, but sometimes every bit counts. During descent, the opposite happens and one engine might need to run at a higher thrust level than ideal. To decouple lateral trim and control from thrust makes sense in those cases.