I'm sure it does depend on the school. Some are "need-blind" (or something really close to that) which means the admissions office does not look at finances at all.
From what I've been told, most schools will only use financial need as a tie breaker. Example: If a school has 6 applicants looking for 2 spots. The 6 applicants have very similar test scores/grades/essays/etc. the school might pick the 2 that did not apply for aid.
My recommendation is to apply for Financial aid because you probably will need it. If your profile looks good enough, they won't reject you just for asking for aid.