If it draws too much current, a local protective device will blow. In the interim few cycles then the local network will not even hiccup.
In the interim few cycles the high starting current WILL dip the local mains voltage.
In a transformer the inrush current is limited to one or two cycles at the most before impedance to the sine wave voltage becomes effective and the low resistance of the winding no longer dictates the current. Local protective devices on circuits supplying transformers of more than 500 watts often have to be changed to ones that are slow to react.
In a motor the "impedence" to AC is dependent on the motor rotating. The effect is the rotating motor generates a voltage, known as back EMF, that is opposed to the applied voltage thus reducing the current. If the motor is stalled or running below design speed then the back EMF is zero or too small and the current is excessive. That is is why large motors have starting gear to externally limit the current until the motor is at speed.
Anyway, that's all for me on this one.
That is good to hear as up until now your information on this thread has been incorrect and your advice if followed could put the original poster at risk of disconnection.