No, she just wants him gone. I have no idea why people thinking this. She has entirely given up on him not only as a son but as a PERSON as well. So anyone is fine as long as they take him.
To be clear, when I said grandkids, I meant getting laid and just that.
But I think you're reaching when stating he wants him gone. First, he doesn't have to get married nor get a girl to leave the house. She can arrange for him to live elsewhere once he's done with high school.
Second, consider this: let's say he gets Agawa, or any other classmate who is still a minor, as a girlfriend, how exactly is that going to get him gone? He's not going to start living at his girlfriend's house if she's a minor so he's not going to be gone anytime soon. If she wanted him gone, then she'd favour the teacher (instead of Agawa and company) because she's independent and he could live with her.
In fact, she's not even asking about whether they'd want to be his girlfriend (because she figures he's that much of a loser), so at this point she just figures it's great if he's just getting laid and I doubt there's anything beyond that. Look at her view on what a man should do if a woman invites him to dinner; she thinks the man needs to plow the woman in that situation. She's a weird person, and whatever logic you're pegging on her, it's clearly not right.
She just expected him to die a virgin, instead of being a man and plowing women. Maybe there's a reason we've yet to see his father (iirc)...