In this case, yes. 2 skid patches is what you'll get.
Since each pedal rotation causes the rear wheel to rotate 3 times, 1/2 pedal rotation will produce 1-1/2 rear wheel rotations -
If, however you were for some reason running 38-19 or 36-18 or some other combination that created a wheel to pedal rotation ratio of 2-1, then ambidextrous skidding wouldn't help, because 1/2 pedal rotation would produce 1 wheel rotation.
If you like the ratio don't bother getting a new cog - just be sure that occasionally you loosen the rear track nuts, pull the chain off the cog, rotate the rear wheel a little bit, then tighten up the chain and track nuts again. That way you'll be applying the uneven wear to different sections of the tire. It will take about a minute.