Dropping power factor but keeping same watts will result in higher VA which means higher current if volts is same.
Adding power factor correction to a motor circuit near the motor would mean you still have approximately same watts consumed by the motor, but the corrected PF reduces VA on the branch circuit/feeder, which will reduce voltage drop on those conductors.
I still think VD is going to be based more on VA and a lower power factor will mean more VA are present.
Same amps, different power factor, means different voltage drop.