You CAN submit your application in June and then take the MCAT in August. AMCAS will go ahead and process your application even w/out the scores and send the available info to schools. Go ahead and start getting letters written NOW. Professors will put it off and before you know it, it'll be June. Yes, you'll have to send in your recs once the schools send you secondaries and ask for it. I'm in a rush, but hopefully this helped!
Oh, and once AMCAS gets your scores in October, they'll forward it to your schools.