Just in case anyone's curious, I tested four guitars today with a multimeter.
Late 90s Fender American Deluxe Telecaster (with Fender tuners)
1999 Taylor 710CE (with Grover tuners)
2004? Squier Bronco Bass (I have no idea.)
2010 Xaviere XV870 (with, I assume, Guitar Fetish's strat style tuners)
I tested electrical continuity from the midpoint of a string to every place I could think of on the tuners. Successful everywhere on the Tele, the Taylor, and the Xaviere. On the Squier, I did not have electrical continuity to two of the four buttons, but DID have continuity everyplace else on the tuners, including the housing, and (of course) the shaft.
So this should work. And I can't think of any reason not to try it The little wiring channels I make will be invisible, and I'm going to use a headplate anyway. Might as well try it.