It will be most likely in the plane of the solar system. The plane of the solar system lines up pretty well with the plane of the Milky Way. I'd expect that most rouge objects are somewhat in that plane. So the probability for objects in or near the solar plane will be higher than those perpendicular to the plane.
As what would happen, there are some simulators out there like Universe Sandbox. If anyone has one of these they could run some simulations for us.