No.
They're kinda just there...
Which sucks, but by nature they're optional and I don't think Arc would want to punish players for having (or not having) kids.
I mean, just imagine, first thing someone going against the MC would do is go after his kids or his women.
It is really a shame, in my opinion girls like Kana and Pixie would have the most impact from having a kid.
But it's the price to pay.