No, please read my comment again If you point the camera down and rotate the ballhead 360 degrees, I think it is clear that you would capture a circle from around the tripod.
However, If the rotation is not done around the base of the ballhead, but around the base of the camera (as with the PCL-1 rotating clamp), then you get an image which is side-to-side (in image space). To visualize this, just think of loosening the camera a little on the ballhead, and turning the camera.
Here is a link to the BH-40-PCL you need (plus an L-bracket).
If you point the camera down and rotate the ballhead 360 degrees, I think it is clear that you would capture a circle from around the tripod.