Theoretically, Ike would have if Greil haven't abandoned his title. Surely, Ike should have been possibly a noble himself for being the son of the infamous Four Riders. But due to his actions of leaving Daien he is declared no longer nobility so Ike shouldn't be noble at all because he wasn't born into a ruling family as he was possibly meant to. Also, Greil probably abandoned his titles long before Ike was even born.