^The scene was scripted but not filmed. I remember reading the text of the scene at some point. It was a good scene, though it wasn't necessary to the film so I understand why it was left out. Although I think it came toward the end of the film and didn't involve the young Kirk.
The scene can be found in this early (and F-bomb laced, for those with sensitive ears/eyes) script here, for anyone interested: http://www.imsdb.com/scripts/Star-Trek.html