Does the direction of counter-rotating props affect efficiency?
It might. Depending on how close to the wingtips your props are.

If you put the props right at the wingtips, then the conventional rotation to minimize precession and torque actually decreases efficiency by promoting tip vortex (the direction of the prop is the same as tip vortex thereby adding to tip vortex). This reduces lift for the same amount of airspeed.

On the other hand, rotating it the other way round - away from each other - reduces tip vortex by twisting the slipstream the opposite direction as the tip vortex. This increases lift (technically, it reduces the reduction of lift due to tip vortex) for the same amount of airspeed.

One plane that exploited this was the Vought XF5U - the Flying Pancake. The direction of prop rotation is fairly obvious in this picture:



The interesting result of this was that even though the XF5U had very short wingspan it could do short take-offs.