The Black Carapace (along with the other implants) were described in the first Index Astartes article. It was described as looking like a film of black plastic, which was planted directly beneath the skin of the Marine's torso. The Carapace would then harden and be fitted with neural sensors and transfusion points, allowing the Marine to directly interface with his armour.
As such the Black Carapace could never be removed, being a part of the Marine them self, but it would have no affect apart from when the Marine needs to wear and make use of his armour. So no, they don't have sub-dermal implanted armour plates.
Incidentally I have been writing some short stories about a group of Marines who seldom use Power armour except for special circumstances, and usually wear Astartes Scout Carapace armour, but that is just by the by.