Sure they can act. Acting with knives will be fairly difficult, now, but using the big AP surplus to fuel Charge followed by Close Combat, Run Away, Bluff (demanding surrender when helpless is a well known tactic for Captain Kirk, frex), or even just scraping stones from the ground and throwing them. It is like an animist freeing spirits from their bindings to get their full AP, since that animist PC has a limited supply of spirits and fetishes.
Determining when they run out of arrows will be a narrator decision, since low bid moves will include threatening to throw the knife or pulling and aiming the bow at an opponent without shooting. All it takes is a decision to do so, announced before the session.
Of course, it can become a bookkeeping nightmare if the PC has more than one quiver, and seems a bit more simulationist than the authors want, but if Narrators can eliminate rules or distinctions if they chose, it seems odd that they cannot add more complexity, too.
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