I do, but for me anyway it's not because of handedness - it's to do with the throttle.
When countersteering I naturally push on the inner bar rather than pull on the outer bar as some seem to. This means I'm slightly less inclined to push as much on the throttle itself = less countersteering = larger chicken strip on the right.
I guess it shows I have more concern for fine throttle control that I have fear for my wonky knee, and that's the left one that I seem to be quite happy to bank towards!
Hey, its been broken before it's had the practise, I'd rather keep the right one pristine for comparison's sake!