It happened to Trinimac and possibly Meridia.
They were Et'Ada, and powerful ones at that. All that proves is that one type of Et'Ada can become another.
This actually confuses me, though. Malacath is Triminac, who helped create the Mundus. Therefore Triminac, and by extension, Malacath is not a Daedra, but an Aedra. That means that Malacath can not possibly be a Daedra, unless the split personality thing can be translating into Triminac contributing, but the other side of him, Malacath did not. That means that there is an Aedra and a Daedra within the same being.
Sorry, just rambling.
But back to the point, the CoC can not become a Daedra, but can he become a Daedric Prince? Maybe, as he has taken on the mantle of an entire persona. That may mean that the CoC is not the CoC anymore, but Sheogorath, in the same way that Jygallyg was not Jygallyg but Sheo. And Jyg is a heck of a lot more powerful that the CoC.