sinewave input input induction motor
Yes, ideally the currents will be sinusoidal. There may be some distortion, but look at the equivalent circuit of an induction machine. 



There's nothing non-linear there in steady-state so the current should be sinusoidal. The phase relationship with the voltage will depend on the power factor resulting from the equivalent impedance at the operating point.  Of course transient loads will cause non-sinusoidal transient currents.