Thought Experiment: spinning ping-pong ball with forward motion on International Space Station. What would Happen? Forward moving ping-pong ball with a with a certain rotation/spin in zero G, 1 atmosphere. Would magnus effect cause Fibonacci spiral?
If you did this experiment in a space station would the ball 'orbit in a circular fashion. The ball would have to be spinning at several thousand rpm though. 
I’m assuming it would decay into an inward spiraling orbit, similar to a Fibonacci spiral. But it will lose most of the angular momentum, before it loses all of its forward momentum so path would start to straighten and spiral back out into a straight line. 
 A: The motion of an object's center of mass is only affected by external forces, so if there were no significant differences in the external forces the spin shouldn't affect the path, see my answer here). But you clarified that you were asking about curveballs, and those are explained in terms of the fact that the spin of the ball changes the external force from the air on the ball, so I think this should still work in zero G. As explained here, the spin's interaction with the airflow creates different pressure on different sides of the ball, leading to a net Magnus force at a right angle to the ball's velocity. Since circular orbits are possible in any situation where the net force is always perpendicular to the direction of motion, it would be possible for the ball to orbit in a circle if the magnus force were the only force acting on it as it traveled, but there is also a drag force which is pointing in the opposite direction to the motion, so I think realistically you would have something more like a decaying orbit spiraling inward. If anyone wants to do some calculations of the relative magnitude of the drag and Magnus forces, equations can be found here along with realistic values for various parameters in the case of a baseball (not a ping-pong ball).
