You could guess the system, depending on the ship's J-Drive and local astrography, but it would be tough to predict where in the system the ship was targeting. If you could combine that with sensor readouts, maybe you could narrow it down further.If jump direction is determined by the angle of the starship's nose, there aren't that many destinations to guess at.
That also raises the question of whether the ship can reorient itself in jumpspace or if they are facing the same direction when they exit. If they are facing the same direction and have to point towards their destination on jump, it has implications for naval tactics, since you would probably want your spinal mounts pointed at the enemy as quickly as possible. I know: It doesn't take that long to bring even a dreadnought around, but if you anticipate going into a hot situation (I know, tough to predict), coming out with your guns pointing in the right direction could get you an extra salvo.