Voltage drop will _reduce_ the initial inrush current to the motor, not increase it. The inrush current is roughly proportional to the applied voltage.
However the available torque is proportional to the square of the applied voltage, so voltage drop can greatly increase the acceleration time of the load, and increase the 'I square T' that the conductors and breaker need to deal with.
Additionally, once the motor is in the low slip operating region, reduced supply voltage will generally mean increased current flow, at least for AC motors.
-Jon
