No. But if the center of gravity is lower than the bottom of the wing, the plane will be stable when balanced upright, and very unstable if balanced inverted. Vice versa if the CG is higher than the top of the wing. So people generally balance high-wing planes upright and low-wing planes upside down. But the balance point will be the same either way.
With a Vanessa rig, you can do it either way with any plane.