Zoggy Grav
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No, Xenocrat is correct. The attack isn't actually a weapon, it's only "treated" as a battleglove during the attack itself. Unarmed strike is a basic weapon with a level of "none," so it can't hold any fusions.
Your GM is of course free to houserule it; I don't think it would be overpowered per se, but being able to apply fusions to a weapon that costs you nothing somewhat runs counter to the intent of the system.