I'm probably under thinking this, but wouldn't the overall momentum of the debris be conserved so you'd have a bias in debris velocity in whatever direction the original objects were orbiting (presumably not random)?
I would assume that as the debris cloud became more biased in one direction, it would be more and more likely to encounter new debris coming in a different direction.
This would be a really fun simulation to run
At least at geosynchronous altitude it seems like it would be significantly biased in the direction of Earth's rotation, especially along geostationary orbit.