<p>hijklm: I think this is what you are looking for. 
There are always exceptions, but in general for non-legacy, non-recruited athlete, non URM or development case, elite boarding schools help a great deal in landing you a “top 25” college, but they don’t help (and possibly hurt your chance) if you are shooting for a “top 5”. (*top 25/top 5 according to us news ranking). Doesn’t mean it can’t happen for your “unhooked” kid but it will NOT be any easier than from a good PS.</p>