I think basic supply-and-demand economics could dictate that the answer to your question could be "yes" but with a catch...
Before Southwest announced and implemented the free Sameday Standby benefits to all fare classes, the fares and availability shown on the "Select Flights" page 24 hours prior to departure often gave me a clue of how full the flight might be. Keyword: might.
If I saw a bunch of red "X Left's" combined with unavailable WGA/WGA+ fares and high Anytime/Business Select fares for my booked flight, that usually signaled to me that the odds of that flight being completely full were much higher and to prepare accordingly. However, more recently, there have been some days where I've checked this page 24 hours prior to departure and there were no red "X Left's" with all fare classes available for reasonable last-minute prices. I've assumed there was going to be plenty of room on the plane only to arrive at the airport the next day to learn that the flight is going to be full. The reverse has happened in some cases too. I think the free Same-day Standby benefit may have something to do with this.
