I'd be a little concerned about long the process takes, since it has to happen before publication. A several month delay would wreak havoc on a lot of indie publishing schedules. (I have no experience with the LCCN process, but the Copyright Office is getting progressively slower. I think none of these offices have gotten expanded personnel to deal with the expanded workload.)
It's also worth noting that many librarians just aren't interested in self-published books. The people I know who have books in libraries have them in local libraries where they personally pitched the librarian. Librarians (if they still have a budget for it) spend a lot of time on new acquisitions, but they obviously don't read every book that comes out (or listen to every indie pitch). Many are reliant on reviews by organizations that typically don't review self-published books. Many still use publishing status as a screening mechanism.
In other words, I'd do some research on how long the process takes and how much of your time and money goes into it before making the jump. It would also be nice to hear if anyone has before and after stories. ("I got that LCCN, and those library sales started pouring in.") I'm sure the people who do get library placements probably have an LCCN, but I'd like to see more evidence that getting an LCCN has a positive effect on library sales for the average author.