cv doesn't control settlement: it just controls the rate of settlement, i.e. it is a time parameter. cv relates to the time it takes water to flow out of the material. With a larger cv you will finish primary consolidation more quickly, but your overall settlement for this stage shouldn't change. Depending on the model, you might initiate more total settlement if creep starts earlier - but that would be a fault with the model since creep goes on even throughout primary consolidation, so the total amount of creep should be (pretty much) the same, regardless of cv.
I think it is reasonable to expect that soil with significant air voids would settle more rapidly than soil with voids full of fluid: there is no fluid pressure to keep the void space open. However, I'm not sure on how this might be quantified. There is a book on unsaturated soil mechanics by Lu and Likos - there might be some information in this book in the sections relating to hydraulic conductivity, k (the correct term for what geotechnical engineers call 'permeability'; kv (or kh) is related to cv (or ch) by a standard equation). I've been meaning to read this book for a while, but haven't got round to it. If you do find something out, I'd be keen to hear what the conclusion to this is.