I went on a couple hour ride today and was thinking about this some more. Imagine that you are riding and you have both of your arms and shoulders rigid, so they stay the same length. Then if you lean with your upper body to the left, you left hand has to push and your right hand has to pull to keep them the same length. So you end up turning your handlebars to the right to turn left if you lean this way. See diagrams below for clarification.imageimage

So it is possible to "think about leaning" and actually be counter steering, but it's still not a good idea.