Does running a 220v synchronous motor on 110v (no load) create overheating problems?

 

Yes, it will run hotter.
Any motor, AC or DC will need some power to keep it rotating even under no load.
At half the rated voltage, the current requirement will double.
Any resistive component in the electrical path will dissipate 4 times the heat that it would when running on the rated voltage.

 

Most likely it will fall to reach its synchronous speed.

 

Does running a 220v synchronous motor on 110v (no load) create overheating problems?

I have done that and the problem was not heating but rather not enough torque to drive the time switch. At half the voltage there is also half the current and thus a quarter of the power. That leads to much less torque.
Note that this applies to the small SYNCHRONOUS motors. It does not apply to fractional HP induction type motors, or other types. In addition, at least for the small clock-types of synchronous motors, the current is limited by the inductive reactance and not by the counter EMF. So heating will not be the problem.