Don't think that is going to happen. Those are personally changes for Ashe, which also will change her actions and behaviour. They don't change the people around her like that.
Sure Ashe will have some new ways to solve challenges and how to act, but just because she will be more assertive in the Siren route than on the Kitten one does not mean Natasha will stop being a top who wants to fuck Ashe's ass.
I believe it will be more like Ashe will "force" any relationship with Natasha (if any) to start from a more healthy place instead of one of blackmail.
At least that was my understanding of Morrigan's post about the routes.