For some schools it may matter regardless. I remember multiple schools that ask if you have any connections to the institution (USC, Penn for instance).
I think they largely ask this to get a sense of how strong your interest is. If your parent went there, the school may feel that you’re applying because you know the school and see yourself as a good fit, even if you grew up across the country or something. And for a school like USC, they have extremely strong allegiances to alumni
Now, I think usually this would help in the sense that it would make you seem like not another random applicant. An adcom might read your app with greater attention— but the rest would be on you.
But if your parent donates a significant amount and contributes to the school in substantive ways, then I think it would actively boost your application to the school.