If I understand your question correctly, I believe that flipping the horizontal knife holder rotates the vise on the same plane (or axis) as the rod centerline, so there should be no change in the relationship between the shape of the edge and the rod’s rotational axis. It will be reversed but not otherwise altered.
As a side note, I see two major benefits in the vertical edge orientation over systems that use the horizontal configuration. The first is the access for viewing the edge. When using a hand-held microscope, a loupe or an overhead light source, both bevels and the apex are easily viewed. It also helps you to see the entire scope of a specific point of damage. The second advantage lies in the ability to use alternating strokes when attempting to remove burrs, stropping or when creating microbevels.
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