Yes, the black part of Chaga can be used, and in fact, it is one of the most potent parts of the mushroom. This is because the black outer part of Chaga—often called the sclerotium—is rich in a pigment known as melanin, which has high antioxidant properties. This is what gives Chaga its dark color.
However, it's worth noting that the inner part of Chaga also contains beneficial compounds like polysaccharides and betulinic acid, so the whole mushroom is usually used to prepare Chaga tea or extracts.