Whoever created Cherokee Carbon crossed Cherokee Purple and Carbon as you said. Cherokee Purple and Carbon both are stable varieties; they'll grow true from seed. But when you cross them, you end up with a hybrid. The first generation of seeds from tomatoes from the cross-pollinated plant will all produce the same plants/fruit when you plant them, and these first-generation seeds are the ones sold as "Cherokee Carbon" seeds. But then if you save seeds from the tomatoes on the plants you grow from "Cherokee Carbon" seeds, the plants (and their fruits) you grow from those seeds will be all over the map as far as characteristics. This is due to how the dominant and recessive genes match up in the subsequent generations (over-simplification).
To create a stable "Cherokee Carbon" tomato, you'd have to grow out several to many generations (5-9 maybe?), selecting for the right characteristics each time, and there's no guarantee you'd ever get exactly the right result.
That said, sometimes tomatoes that are released as hybrids actually seem to be stable and grow true from saved seed. People have said that about the Brandy Boy hybrid, for example. So it's possible that Cherokee Carbon is stable. I haven't seen anyone report on results of growing it from saved seed.
I've grown Cherokee Carbon three years now and love it -- healthy plant that holds up well to foliage disease, great production, relatively uniform fruit with little cracking or catfacing, and delicious. I saved seeds from my last time growing it and hope to see what grows from them some day when I have more garden space and time for experiments.
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