No it wouldn't. Part of the whole point of the Kobayashi Maru scene is that you don't know it's a simulation until Kirk says "Open her up," and the viewscreen pulls back. Panning down to the Enterprise flying through space maintains the illusion. Panning down to Earth, then zooming in on Starfleet Academy in San Francisco ruins the surprise before you even get there.
Yeh but it also makes no sense - the Enterprise isn't in space. It's a bridge simulator with a viewscreen.