Yes, but they don't have a normal relationship of a loving mother&daugher.
Aika becomes a full on slut, who is used as just a plaything by her mother. Her mother sends her to fuck the people she wants to gain political influence over, for example. She pretty much works for her mother, like the other non-academy servants. But who knows, maybe her mother does "love" her, in her own perverted sense. But yeah, that's the only ending where they can become a "mother and daughter".
There is an ending, where you DO kill the mother, but then Aika takes her place and becomes the new demon queen, or whatever it's called. During that ending, she is shown to have a sexual relationship with that girl who wears glasses, that her mother used to fuck (I forgot their names, since I haven't played this in over a year), and is also shown to really care for that small, badass black haired loli, who now works for her. Oruzure or whatever her name is. Like, she makes her take breaks, and sleep, eat and whatever. If I remember correctly, it is insinuated that she's grooming her for sex, too.
But yeah, those two are the best "branch-academy" endings you can get with those characters, unfortunately.