When Oceans are in play, can Invader or Dahan pieces remain in the Ocean if they avoid Drowning?

When Oceans are in play, can Invader or Dahan pieces remain in the Ocean if they avoid Drowning?

No, Invaders and Dahan are not allowed to exist in the Ocean long-term. If one manages to get there without being Drowned, move them to the closest legal land after finishing resolution of whatever got them there.
In the base game, the edge-case where this can happen is if Bringer of Dreams and Nightmares uses Vengeance of the Dead (with threshold) on the Ocean itself. A Town/City/Dahan is moved to the Ocean, triggering Ocean In Play which Drowns it. Drowning (destroying) it triggers Vengeance of the Dead. If Bringer deals VotD's "damage" in an adjacent land to "destroy" a Town or Explorer and Push it into the Ocean, Ocean In Play can't trigger again, because actions can't trigger themselves, even indirectly. So the Town/Explorer isn't Drowned.
In theory it can also happen if you use Infinite Vitality (with threshold) on the Ocean then Push Dahan into the Ocean, though that's usually a pointless play.