Pumpo:
During the starting condition yes, the voltage drop will reduce the inrush current proportional to the line voltage drop.
Under a steady HP load condition, the current will increase with a drop in voltage.
IL = HP*746/(1.73*VLL*EFF*PF)
Were
IL = Line current under load
HP= shaft load in Horse power.
VLL= Line to line voltage
EFF = motor efficiency ( regularly it will drop a while with lower voltage)
PF = motor power factor.