I submitted on 6/20. My application was on "hold" until today (6/23), because I attended the same school twice, once as an undergrad and once as a postbacc, and AMCAS wouldn't count my transcript twice! (They also told me NOT to send in a second one...) The transcript arrived on May 11, and since then I've called 7 times and emailed 5 times. Today they finally agreed that something was wrong and they put in a transcript exception request for me. So now my application is "active."
Is it true that July and August are the really heavy months for people submitting? Is June a little less crowded? I hope so... I have no doubt that with five transcripts in their files, AMCAS is just going to go crazy over my application and take forever.