Yes, he is a demon. When he shattered Mar'dum all that fel energy exploded onto him changing him and he became a fel titan of sorts. So he is a demon and has been for aeons.
Eredar are demons, Man'ari Eredar that is so no he is right. Technically his BE DH does have a immortal demon soul, especially if you sacrifice yourself in the DH starting zone. Illidan monologues about it to.