Yes!! Kiryu really... looks up to his dad in canon despite him being awful so having someone to be like "actually, that's fucked up" is exactly what he needs...

Look, he will try to be the best big bro possible if that means buying her things or running her errands, that's what he'll do. Just don't ask him to cook dinner, he's not regaining his A+ ramen cooking skills for a long time (Yakuza is a weird game)

That sounds good to me! Go with whatever you want, Kiryu's going to be a boring, mild-mannered guy for a long time... so feel free to go as crazy as possible. He'd probably imagine a little sister like... tiny and in need of protecting (boy will you be surprised, Kiryu)