No, Bungie said you won't receive any rewards for a quest you've already completed. Check the helo forum post from Bungie
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Even though I haven't completed both subclasses, just one and got a band? That's poo poo
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For the subclass quest you haven't finished, there is hope. If you finish it after 09/15 you'll get a bond and an emblem. However, the quest you've already finished won't give you the subclass specific emblem and it is possible that you will lose the bond as well because Bungie is deleting stuff from player inventorys right now (Like the suros and CE stuff).