I can imagine it both ways, though. I can certainly imagine him hesitating to complete the Vow--remember, when he agreed to it readily it was only with the condition that he protect Draco, which he was happy to do--but when the "complete Draco's task" condition is tagged onto the end, he knows that to back down then--he knows that even that little bit of hesitation--will condemn him in Bella and Narcissa's eyes, and Bella is dangerous. So if he knows what the task is, he still--he especially--needs to agree, because it's something any loyal DE would readily agree to do. And he hesitates because he thinks, "Oh, f**k, I've just killed myself. But it's not like I thought I'd get out of this alive anyway, sigh." And he completes the vow.