I think it could but does not necessarily have to reach a station. The elevator just has to clear the atmosphere, right? As they say: once you're in orbit, you're halfway to anywhere.
Presumably the elevator would lift cargo, fuel, maybe even the actual rocket into orbit where maneuvering is easier. Once it's in space and in orbit, substantially less fuel is required maneuver.
I think you might be talking about something else than a "space elevator"? A space elevator would just go up and down as far as I understand, not horizontally, and if you wanna end up in orbit, you need horizontal movement, not vertical.
