The funny thing is, at least according to a legal admin I talked to at PC, is that they don't even actually run you through NCIC or anything until 6 weeks (or was it 60 days??) prior to staging. So there really is no rush to get it in like they make it sound! Although, I guess that if you have something showing, the sooner the better so you can submit explanations!
I used to run these kinds of checks myself, and it literally takes minutes to get a return when you run someone (or even faster).