Yes, props on planes do counter rotate. Otherwise, an enormous amount of rudder would be required to control the plane.
The air drag also produces roll. That cancels out when they counter-rotate, adds up when they rotate the same way.
Boats have a similar problem. In addition to roll from prop drag, the bottom of the prop produces more side-thrust than the top. (Think of it as 'walking along the bottom.") So dual-prop power boats counter-rotate to cancel it out. (Some have a gearbox, others have one engine with a modified camshaft so they spin backward.) It's especially noticable when just starting to back a sailboat (single-prop auxiliary engine and rudder) out of a slip: The effect is more pronounced in reverse (where the prop is less efficient and thus has more drag) and when just starting you have no "way", so the rudder does nothing.
Also, dual counter rotating aircraft engines tend to yaw when you loose power in one engine. In adverse circumstances especially on takeoffs, they are known to yaw, then roll right into the ground.
The yaw is from the one-sided loss of thrust. Rotation direction doesn't matter for that.
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Regardless: If you have two identical mills on a single tower, having them counter-rotate will cancel out a lot of small stuff - including maybe some of the sound and vibration if they sync themselves up. (And they're guaranteed to do that if you hook the alternators together upstream of the rectifier. B-) )