It seems that the tips of the fan of a turbofan engine can and do break the sound barrier:
The GE-90 has a fan diameter of 3124 mm and a rotational speed of 3475 RPM. Their circumferential velocity is d·π·57.917 = 568 m/s or Mach 1.67 at sea level and ISO atmosphere.
Peter KämpfPeter Kämpf's answer
While, on a propeller driven aircraft, it seems that having the prop tips exceed the speed of sound is a bad thing - Can turboprop blades break the sound barrier?Can turboprop blades break the sound barrier?
Why is it that exceeding the speed of sound is acceptable in one situation but not the other?