^ No, because they used the exact same FX for every type of orbit in every episode of TOS. The only thing that changed is the color of the planet.
Addition - the only things that changed are the color and rotation direction
of the planet. Sometimes it went with the Enterprise's direction of travel and sometimes it did not.
I would need to see an example of that, since as far as I know this is not the case.
Here are a few that I recently remembered seeing that you can see the different rotation FX used in:
The Mark of Gideon
-> planet spinning counterclockwise (if viewing axis from the top of the screen down)
-> planet spinning clockwise (axis tilted toward viewer and to the left)
-> planet spinning counterclockwise (axis tilted to the right and similar to Enemy Within since it is probably a reverse angle as you described)
-> planet spinning clockwise (axis tilted to the left)