Question, can servos "leak" power?

Hi LMR! If you haven't seen my robot MAEP already, it has two power supplies, one for the motors and one for the Arduino. I decided to add an LED indicator to show when power is being supplied to the motors (which are servos). The LED is just connected in series with a 1k resistor to the power lines from the motor power supply, a 4.8V NiCad battery. As you expect, the LED is off when motor power is off and on when the motor power is on. But when just the Arduino is on and not the motors, the LED is lit dimly, and changes brightness as I wave my hand over the sensors. This seems to indicate that the servos are leaking power into the motor power rail when given a signal from the Arduino. Has anyone else heard of this or noticed it? And will it cause any problems? My initial guess is no, because it's working fine so far, but I'd like to hear from someone more experienced :), so please answer if you have any insight.

Servos always use power -

It is usually pretty minimal in the stationary state although sometimes it can be a bit more if the encoder cannot make a decision as to where the servo should be,  such as if the position is between ‘steps’ on the servo.  I’m speaking from my RC days here.  It’s not  problem.