I went complete at UT within 8 days of getting the Application Received email. However, I applied a while back, so it may have been before a rush of applications.
UCLA...ugh. Good luck with that one! I sent mine on 10/27 and finally called the other day to confirm because I hadn't gotten an Application Received or Complete email. I finally got the complete email later in the same day that I called. Give it a good month there.