[shovel]

limited slip diffs, whether they're clutch (cone, disc, or 'phantom') or helical or even hydraulic piston (varilok) or dog-clutch (Aussie, Detroit, etc) don't have any way of affecting mileage when you're traveling in a straight line with equal pressure in your tires, because the business parts of the system are all built into the carrier, and essentially static when there's no difference in rotational speed between the left and right wheels.

When you turn a corner, clutch type LSD's necessarily scrub but as serialk11r points out, if they really created much drag they'd need cooling because that energy has to go somewhere. Helical systems are more about leverage than friction and when there's very little difference in the torque distribution between wheels (turning a corner, both wheels on pavement, there is wheel speed difference but not a drastic difference in torque delivery, both are receiving power from the engine pushing the vehicle forward) - they don't have any more excuse to create drag than the gears in your transmission.

I can think of no time a traction aid would affect mileage, except by improving it when you would have been stuck & spinning a wheel, and instead you're moving.