She does know, because it's one of the many ways in which they overlap. A determination to get home somehow. A need to find the Door, to do something which stops them feeling so powerless under the gods' rule. But because Kate knows that, she knows just as well how important Carlisle is to Glacius — she feels shades of that very thing when she's with Ignis. A desire to just... stay here, where she can have that happiness and peace which comes from their relationship.

"Doubt he'd leave this place without you." Not by choice, anyway. That much she feels certain of. Glacius' loyalty burns fiercely to his friends, to his people, but most of all... to this man, right here.