My gut feeling says that CNBG probably can breed with HBG, question is, will they? I haven't run across any studies confirming this, it's just my interpretation of the two fish.
I have a few RES x BG hybrids in my ponds, but I don't see it happening very often. I think water clarity, and the availability of suitable partners probably plays a role in the occurrences of natural hybridization.
I think the CNBG crossing with the BG would be a more typical scenario, although I'm not sure what benefits, if any, would stand to be gained from such a union. Perhaps the long awaited possibility of a more cold tolerant coppernose? Maybe, but certainly not guaranteed.