Is there any way to use the saturation harmonics to determine the rated voltage of a induction motor?
Regardless of load, the saturation of the core increases as the voltage increases. Above rated voltage the saturation increases more rapidly. The effect can be seen more easily at no-load because most of the motor current measured at no-load is stator magnetization current. The change in the slope of the current vs. voltage curve gives an indication that the voltage is increasing above rated voltage. The change is not sufficiently dramatic to definitively reveal the rated voltage if it is not known.

I don't think that there is any reason to believe that saturation harmonics change dramatically at rated voltage. It is more likely that they change gradually as does saturation due to the fundamental voltage.