Success or failure Link is determined to hop a portal home. He is the Hero Chosen by the Gods, after all! He will never forgive himself if he's unable to fulfill his destiny.

If the plan is a failure Ardyn intends to stick around. If it succeeds he is willing to stay behind to operate the portal. He should have met with oblivion already. There is nothing for him back home and he doesn't feel like dragging out his long suffering existence in new worlds. If the world surrounding Beacon seems determined to wake up and live again he'll linger in this world to protect it from World Eaters until his lantern finally breaks.