This is a bit of a moving target, in that the rules change. Under the old hiring leadership at United, the LOR's were reviewed when the computer spit your name out as a potential interviewee, and they carried weight--and not just the ones from CPs. They were then not reviewed again until after your interview.

This may or may not still be the case, but I would assume that the LORs are looked at twice. Have 'em early, and make sure they will be good.