It does, but just barely. Unless your parents have been speakers, or have donated large sums of cash to the school, I wouldn't say it does much. Legacy is slightly more looked upon for Harvard, Yale, and Princeton. Just slightly.
If you look at the Common Data Set for any of the Ivy League, they show how little it matters. However don't get me wrong, such a relation can do nothing but help you. Albeit, it might not be much help, but it might be enough.