No, I don't see such a scene as likely either, and I'd agree that it would be very out of place in the game and in any of the routes. I think it's fair to say that one wouldn't bring Natasha home to meet one's mother! Although, now I think about it, maybe Cuckquean Ashe should

.
Is there an Natasha enemy path? I don't know anything about that but I can see why some might dislike having her pop up again. I guess though it fits into the anti-duplo discrimination background of the world and Ashe's difficult life. It might be strange for Natasha to simply disappear if Ashe turns her down, given Natasha's character.
EDIT: Just ran through the game again. Stopped Natasha during the patdown, ran away from her at the gym and kicked her in the face during the cleaning scene. Still got on to the Kitten route, but yeah, does seem likely that Ashe has made an enemy there.
I guess it's all dramatic tension in the end.