I don't believe adding more digits of PI would help even a tiny bit with course corrections. As planets/moons/asteroids are not perfectly smooth and evenly dense spheres, any slingshot maneuver used to accelerate/decelerate will require course corrections. And of course, very tiny effects from microgravity, solar wind, space dust, etc. add up over sufficiently long periods of time, requiring more course corrections. Plus thrusters aren't 100% perfect either, and neither are the instruments used to measure position/orientation. There are so many different possible causes for inaccuracy, and I suspect every one of them is orders of magnitude larger than using a 64-bit float for PI.
Doing a little math... Assuming Google gave me the correct answer, the average distance between the sun and Pluto is roughly 5,906,380,000,000 meters (13 digits). So in a 3D chart with the origin at the center of the solar system, everything out to Pluto's orbit could be modeled accurately down to the centimeter level with 64-bit floats (assuming we had modeling data that precise, which we don't). Regardless, no matter how many digits of PI you use to attempt to perfectly aim an "unguided rock" toward Pluto, its path is not going to be accurate down to the centimeter level by the time it gets there. ;-)
P.S. - Why on Earth would you EVER want someone to toss unguided rocks around the solar system. IMO one of the best lines ever in a sci-fi novel... Q: "What are we going to do, throw rocks at them?" A: "Yes."