No special bonus is gained by the wearing of multiple pieces of this set.
Bad'Ushra in Moonfield Hamlet will exchange Marks of Manaar for Legendary armor. The head, chest, and hands slots (there is no legs appearance armor as the legs are covered by the robe) are expected to be filled with instance drops and are offered only as appearance items so characters may obtain a consistent look.
The only armor piece in this set that actually shows are the slippers. See the Demoncloth Set for appearance.