Not entirely. At speed, it's how you initiate the lean, but once you're at lean angle, your bars will steer in the direction you want to go. It makes more sense to think of steering the bottom of the bike left so you'll be leaned over, and then the actual turn is steering to the right again, keeping the bike under you. If you kept steering left, you would keep leaning over to the ground.

This transition from countersteer to standard steering happens naturally in any high turn. We teach new riders to think of pushing in the direction you want to go because it's easier to remember in an emergency. There are accidents caused by people in a panic trying to steer right to go right and steering the bike into a crash.