This card's second ability produces a global, continuous effect that stays in play for the whole turn and constantly checks your J-ruler's name. So, if you activate it without having "Melgis, the One Charmed by the Demon Sword" on your field, its second effect ("if it's Melgis...") will still provide Imperishable and a reduction in the God's Art cost during the same turn even if you play the judgment process of Melgis later in the turn.