This card's second ability produces a global, "cloud" effect that stays in play for the whole turn and constantly checks your J-Ruler's name. So, if you activate it without having "Pricia, the Commander of Sacred Beasts" on your field, its second effect ("if it's Pricia...") will still provide Imperishable during the same turn if you play the judgment process of Pricia later in the turn.
If Horn of Sacred Beasts's banish effect targets the player controlling Horn of Sacred Beasts, Horn of Sacred Beasts will be in the graveyard before the ability resolves, and will shuffle itself in as well.