This year because of the AMCAS disaster, I think that anyone who submitted between June 18th and July 31st all were in the first batch of secondaries sent out by the schools. I submitted on July 16th and received all of my secondaries in early to mid-August because most schools, even those that traditionally screen, were just sending out secondaries to those who had listed them on their AMCAS just to get the application ball rolling at their level. I had started my app on May 24th, soon after it was first released but was delayed by the server hangups. I definitely recommend this route if you can. However, I agree with Coalboy that if you are preparing for the August MCAT, don't try to do both concurrently. Yet, it is possible that if you have all of you materials together when the application first comes out (i.e. have transcripts, lists of EC's with summaries, essays written, etc.), then you can get your AMCAS done early.
FYI. I interviewed at two schools very early where I had gotten my application complete early (that means sending in the secondary because they weren't waiting for verification by AMCAS). I sat on two secondaries and haven't heard a peep from those schools. Lesson learned: get those secondaries in early!!
Hope this helps.