Well, it depends. I mean, some people who submitted as late as June 1st were included with the first round of transmission to medical schools, which was June 13th. Others (like myself) submitted in May and were also included in this group. As well, keep in mind that TMDSAS will transmit your application without your MCAT or LOR's, but medical schools might not consider you. I've heard it both ways regarding LOR's and getting interviews. Some schools staunchly say they will not interview you without them, and some schools will interview you without them. I know I've heard that people with and without LOR's have gotten those first interviews at UTMB.
Hope that helps.
EDIT: Another thing to keep in mind is that even if TMDSAS has received your LOR's, they won't necessarily accompany your application upon processing and transmission to medical schools. In my case, I was processed and transmitted on June 13th, but my letters weren't received by schools until June 25th. I am sure this delay will continue to compound as applications and LOR's continue to roll in at Austin.
-Sean
