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It seems rather inconvenient to have to take the CC off the camera to meter the lights, then put it back on to act as a trigger, but I guess one would just get used to it (or use a seperate CS as trigger).
Yes, you use a CS as the trigger on the camera and keep the CC on your person. I've pretty much relegated my Sekonic to situations that I am not using my Buff lights, but shooting ambient only.
Even in mixed lighting (which I do a lot of), the CC does measure the ambient. You can set it for a small number of specific shutter speeds and it integrates the ambient at those speeds (as any flash meter actually does). It's not as flexible in that area as a general-purpose exposure meter, but then, it's not a general purpose exposure meter--it's intended to be used purely as a flash-control meter.