Absolutely no way are you allowed to use your NPC during an HNM fight.*
*Restrictions on using NPCs during HNM fights are deemed null and void provided that the caller's party has fewer then 6 members, the fight occurs outside of non-ToAU area, Dynamis, Limbus, Sea, Sky, Einherjar, Dragon's Aery (according to the wiki), and so on and so forth. So basically if you can call it in the area, you can use it.