I have been experimenting with different ways to achieve the effect I want.
I uploaded a test here (sorry for the bad file hosting)
http://www.mediafire.com/file/fyfnrjyigzh/CubeTest01.c4d
This is almost what I am looking for. I have the random effector fill up the shape by animating the Sample Distance in the Falloff tab. The biggest problem is I want the shape to be filled from the center and radiate out. This will remove other problems such as the cubes intersecting through one another. I can tell that the effecter is filling up the shape based on the perimeter first and that is not what I want.