Lmao lil bros really be thinking that japan is some fairy land society.
Yes, you'll get a bad record if there was a loud controversy involving you, you'll get a bad record if a background check comes up with info that people you're involved with have a real criminal record (yet sons and daughters of yakuza got in just fine, but that's another matter). Your bad record will be weighed against your good record like extracurricular activities, etc.
And shit like this would only matter if ever if its ivy league type of shit that affects less than 1% of society anyway normies get on just fine. If you don't get in, its because your parents are not high enough in social hierarchy or they didn't pay bribes due, not because of ridiculous shit like whats in the manga that runs on ntr logic, obviously.
Additionally on a real world standpoint...
Speaking from experience, yes schools/academies/colleges can get petty when it comes tou your background and relationship status(and the background of your partner)... And this is considering I came from a country that is "least Asian" in consideration to strictness.
Puh'lease Taro, share with me your story on how you didn't get into college because of your big tiddy delinquent gf. Next thing you'll tell me is that you believe japanese society is a meritocracy too? Real life is not manga. Should have spent more time doing charity and networking instead of playing blue archive and jerking off, I guess.