Counter-canter question?

I'm not sure I understand your question. If what you are asking is how it affects the horse when you circle to the left while on the right lead, then my answer is that it makes it difficult for him to balance himself, but it also is excellent for developing flexibility, and is therefore a useful training exercise.

Add....I believe the horse would switch leads if you did that.

A horse that knows its lead changes would most likely switch to the left lead. For the counter canter (on a trained horse), the bend to the outside shouldn't be drastic. It's more like a continuous reminder by messaging the outside rein and using the inside leg.

when a horse is ridden in a canter on the incorrect bend, it forces them to throw their outside shoulder out to balance themselves. they shift their bodies from side to side as they stride through the circle, and are generally off balance. horses are built to naturally take the inside lead for balance, and when a horse isnt framed and balanced while counter-cantering, it turns into a sloppy mess.

when my horse always does that he get faster and falls into the turns. But my paint also does not have a flying lead change. So i use the crop behind my outside leg to get the back lead.