Weeeelllll, sorta no, but maybe yes.
Reread the OP, and it's a touch more complicated.
The problem the OP will run into is getting the tranistor biased such that a proportional output from the motor leads yeilds a proprtional output from the motor -- effectively, the transistor will *want* to be always on or always off. if the servo controller is pulsing the DC motor to turn the gears, this will work well, otherwise you've got to balance the circuit such that the trasnsitor is not like a floodgate -- open or closed -- but a water spiggot -- turn a little get a little, turn more get a little more.
Benny,
If you want an all-on/all-off control, you can use a circuit similar to this one (listed as "Basic NPN Transistor Switching Circuit"):
http://www.electronics-tutorials.ws/transistor/tran_4.html
hook up the servo's motor leads across the "Vin" and switch, and connect the main motor across the "relay". you'll likely still want the flywheel diode -- it'll protect your transitor from back EMF when you turn the motor off.
If you need proportional control, look into a receiver brick (many have brushed ESCs installed), or a reprogrammable brushless micro ESC -- if you can reflash these, you can edit the source, recompile, and flash to act like a brushed ESC.