"Integrating" is an interesting choice of words. From what I've seen of the integration, nothing of their genes really survive. Nothing of their culture survives. I don't think it's survival at all. They're absorbed, surely, but in the same way an amoeba absorbs some prey... little pieces of the prey move around doing what those pieces always do, at least for a little while. But eventually those pieces stop moving, and get broken down into ever smaller pieces, until nothing of them remains. And it's just a big amoeba.
Not sure what word is a better choice though. Maybe someone can reply with one.