I completed Legendary on my Hunter. The boost says it 'grants associated rewards', and 'a set of armor for the character's class'.
Does this include the new exotics?
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Using a boost completes the base campaign, and not the legendary version of it, and as such, would not grant you the completion bonus for having completed it on Legendary, so you would not get the associated exotic. You would still need to play the Legendary version after the boost in order to get the exotic.