Yes, Virginia, the assumed fact is true.  “Idol” contestants who get pimped in early episodes go much longer than those who do not. Editorials and Articles Archive – WhatNotToSing.com – The American Idol Internet Database

Promotional Piece contestants are, on average, 20.2% more likely to advance each and every week than those in the Late/No Exposure group, given comparable performances. Similarly, Audition-only contestants are 14.0% more likely to advance each week than those who did not have their audition aired.

And, seriously, they have the charts to prove it — both bar and line!