I decided to test all this out by recording the time required for one revolution of the motor with no load. With the auto-adapter (shown above) set to 5V I recorded a time of 9:57.68, and with the 6V regulated battery I recorded 9:57.22. And that was just by eyeballing the position of the gear. I can perform a more precise test but I don't think it's necessary. I think it's clear that the voltage does NOT affect the speed of the motor.

So super-precise voltage regulation isn't necessary for good tracking. Still, there were other reasons to do this...avoiding the purchase of expensive D-size batteries, and to get rid of the separate battery pack. So for anyone who wants to lose the battery pack I'd recommend a 5-cell AA NiMH battery pack and just duck-tape it to the back of the controller.