Please, CoC is not a structural characteristic of a lens, it is the maximum amount of defocusing or unsharpness that will be indistinguishable from a perfectly focused object, based on OUTPUT (will I be able to stress this enough?) size and viewing distance. It is a concept based on the angular resolving power of the human eye. IT HAS NOTING TO DO WITH IMAGE CIRCLE.

Now, in relation to mounting distance, I think there is an indirect relation between it and DOF, but the real factor is pupil magnification. I will try to explain

Pupil is referred to the apparent size of the aperture. Entrance pupil is viewed from the front, exit is viewed from the back of the lens

Pupil magnification is the ratio between exit pupil and entrance pupil

Think of three common lens designs:

- Symmetrical - used typically in normal lenses and most large format lenses, the pupil magnification is 1

- Retro-focus - Typical of wide angle lenses, to allow greater distance from the sensor/film plane and clear the mirror box in DSLR/SLR , pupil magnification is greater than 1

- Tele - Allow for a lens that is shorter than its focal length and so it can be mounted closed to the sensor plane and pupil magnification is less than 1

What is the effect of this?

The Pupil magnification is a factor that does affect DOF and it is included in the complete equations, but it is usually discarded because its effects are only relevant at close focusing distances

The effect of pupil magnification is Inverse to DOF, which means, the greater the pupil magnification (as in retrofocus designs) the smaller the DOF. Since the retrofocus lens will have a greater mounting distance than a symmetrical lens, you can erroneously assume that the change in DOF is due to mounting distance, but it is really due to pupil magnification.

Another effect at close focusing distances: Lens focal length, it turns out that for a given field of view, the longer the lens, the shorter the DOF for the same entrance pupil diameter.

What to consider as a close focusing distance? A rough approximation is 10 times the focal length.