Nope, the initial peak surge current is determined by the DC resistance of the windings; Once the motor begins to turn, the current decreases because the motor is generating a "back EMF" which is in opposition to (but smaller than) the applied voltage. The faster the motor runs, the bigger the back EMF, and the lower the current. If you apply a load (torque) to a running motor, the current increases as the motor shaft begins to slow down (because of the reduction in the generated back EMF).