The developers mentioned in past Q&As that there would be unique dialogue options for characters who are from the Deadfire Archipelagos. They've also mentioned that they would work on integrating background options into dialogues as well.
That said, I highly doubt your character will meet their family in Pillars 2. The Aristocrat option is open to all races, so in order for them to introduce your character's family believably, they'd not only have to come up with versions for each race but also relocate the versions to areas in which the presence of aristocrats of that race would make sense. That's a lot of work to do for one background out of dozens.