Yes. I was doing research the other day on the prokaryote cells within a lobster's antenna and they have a thicker cytoplasm compared to a regular cell wall. And it contains Chitin-glucose outer layer which is a derivative of chitin..so yes.
a cytoskeleton is not an exoskeleton. an exoskeleton is by definition on the outside of the body. the cytoskeleton is inside the cell. the closest thing to an exoskeleton would be the cell wall.