There is no huge demonstration of it or any massive things that point to it, but karma is in place because its shaping Anath's personality. She changes along with the MC. MC is dominate and kinda evil? She is more likely to push for more and more evil actions. If he is kind and nice, she's more likely to sympathize and do kind things. She in story tweaks scenarios, how she goes about it karma will play a role (this is what I am lead to believe but there hasn't been much on that front yet to show it off)
edit: I think its along the lines of something like this (this is me making a guess, based on what I was told, but this is not confirmed), again, just an example: Anath is always on the side of you getting laid and experience, and thus gaining power. Your karma can dictate whether she pushes the girls into scenarios like having you take advantage of them in a callous manner and just in to pump and dump them, or if she goes about it in like trying to set them up to actually fall in love with you