Well, after opening up my test map to try and prove my theory, I found I was entirely correct.
I first took my basic box map, and put two blocks in the center of it, one with a target texture stretched across it so I could stand against my marked corner and look directly at it, so as to assure me that I had the same line of sight during every test. My map ended up looking like Kasperg's first diagram, but with the two floating boxes I mentioned.
On the first compile, I ended up with 271 w_polys. On the second compile, I raised the skybox very, very far up. I got the same w_poly count. Third time around, I placed several boxes and a cylinder with the SKY texture on them, and raised the hight of the skybox even more. In the fourth and final test, I raised the view distance of the map to 7000, just to make sure I was not being limited by it somehow, and there was no change in r_speeds at all.
Thank you, Orpheus, for using my correct title of "master srry".
And raa, I should probably point out that although having a bigger or more complex skybox does not amount to higher r_speeds (unless you having a big skybox actually allows you to have more brushes/models in view), I have heard that it decreases the FPS, however I'm not sure exactly how substantial of a thing this is anymore. Given newer video cards, I doubt you'd even even notice it.
P.S.
Orph, you have now earned the "You're Winner" trophy from me.