Traveller would've "lived" because it's not really alive in an organism way. Vex aren't really living, Hive would "live" because Hive Gods can just spawn more...literally.
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There's no real proof in destiny that the traveller is alive or dead so I'll let it slide. But it's clearly stated that vex have biomass ( white goo) which would be destroyed, leaving them unable to function. And forerunners and easily superior to hive. They've destroyed and recreated the entire galaxy
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Hmm forgot about the white goo.