No, you are not correct. The Olympus C210 was designed for 35mm film cameras (granted, they were fixed-lens "bridge"-type cameras), so it was designed for full frame with a lens set to 110mm. The vignetting issues you have with it are probably because it simply wasn't designed to be matched with any focal lengths other than 110mm.
With screw-on teleconverters, all you're really doing is putting a magnifying glass in front of your lens. That lens isn't part of the lens's optical design, and therefore can cause image quality issues, as well as limit the ability of the lens to focus at one end of its range.
All you really need to worry about is the thread size. So getting one with a 67mm thread to fit your Hexanon is the only spec you need to worry about. However, the image quality of using one of these cheap TCs, especially the higher the magnification factor, may not be great, and isn't going to be at all the same as just using a longer native lens. You'll also be reducing your maximum aperture. And at 500-600mm equivalency, you should probably be looking into some form of stabilization, handholding that combination could get very difficult, especially with manual focus.
You may want to consider saving up to get a used Nikon 70-300 and the FT-1 adapter if you have a moving subject in mind, and can't cough up the $1k for the Nikon 1 70-300.