Does a 230 V (240 V) single-phase motor technically draw twice as much current as the label states?
A 240 volt motor will only be connected to the two live wires, not to neutral, so your example draws 6.6 amps at 240 volts.  If it is connected to operate at 120 volts, it will be connected between one live wire and neutral, and will draw 13.2 amps at 120 volts.

I think it is misleading to say that, in the 240 volt case, the motor draws 6.6 amps from each live wire.  A more correct description would be that it draws 6.6 amps from one live wire, and returns that 6.6 amps through the other live wire.

Using the same terminology, in the 120 volt case, the motor will draw 13.2 amps from the live wire, and return that 13.2 amps through the neutral wire.