My experience would tend to indicate that recommendation letters don't do a lot to speed the process along. I uploaded four when I updated my application in August last year. Two were from Alaska pilots and one was from my current direct supervisor.

What I have learned over the course of the last year is that a strong résumé and a lot of effort to be seen at recruiting events will do a lot more for you than letters with your application. I'd guess that's why they don't take them with the application now - it's just not what they're looking at when they decide who to call.