You could always apply now and put your application through, but at the same time if you do really poorly you may not be able to change it. From what I have been told, once you put your MCAT score through AACPM you can't adjust it, you can really only talk to the admissions committee and tell them you are planning on taking the MCAT again. It takes at least 12 days to get your application verified in August. At least you will be getting your scores back in early September.
Don't take my word as the only answer (obviously) but if you feel confident enough that your MCAT score was above a 23 and your GPA is adequate enough compared to the averages then you could take the risk and apply now just so you can get the two weeks of your application and transcripts being verified out of the way. There is a section on the AACPMS that does give you a box to say that you have taken the MCAT and are awaiting your scores. Don't get your hopes up for any interview invites (except maybe Barry because they do tend to give invites without an MCAT score) since many schools the time table to get verified is much longer the first three weeks of the cycle (August 6th to 27th-ish) than all of September.
Yes, you technically can apply without the MCAT score, but the risk is that if you do get your score back and you don't think it is competitive enough then you may have to contact the schools to tell them your situation. And if you want to take the MCAT again, then you'd have to take the January MCAT which has the added bioschem, physio, and sociology. The way I would look at it are based on what I see as the pros and cons of applying now or the next few days without an MCAT:
Pros: You can save two to three weeks in September to wait for your application to be verified, Could get an interview acceptance just days after your MCAT score is released (as opposed to three weeks after).
Cons: If you bomb the MCAT badly you may get auto rejected without a chance of defending yourself in an interview, you have to shell out the money for the application without knowing how competitive you really are.