I feel like the tricky aspect of doing this is that it's very hard to work on your primary while preparing for the MCAT at the same time. So, you will probably end up submitting it after. And, while it takes 4 weeks to score the MCAT, it can take > 5 weeks to get verified, and let me tell you, it's painful having a good score and wanting to submit secondaries and not being able to. Prewriting is also easier said than done. I guess I think you should consider whether you *really* need that time. I kept pushing it off because of confidence issues and burnout. I psyched myself out so hard that I only took 2 practice tests, 1 7 days before, 1 5 days before. I got a 521 in the end. I ended up studying 3-4 weeks max (very long days) and was flat out unproductive when I pushed it back.
I wasn't on depression medication until late last year, and I was genuinely burned out after graduation, but had I been in a good state, I would have taken the test in January or by the end of June and submitted my app immediately after. It's honestly so stressful to be waiting for responses while people who submitted earlier have 5 IIs or something.
It depends on what the stakes are, for you. I feel like if you budget time well, you could probably write out the activity descriptions, solicit rec letters, and even draft up the personal statement/additional essays over an entire school year, and submit the primary right after the exam, prewrite secondaries, and be complete by the end of August. Or you could try to do it all after the test and probably still be complete by August. That being said, gonnif has a point about making a school list. Mine was very restricted to start with, so it was easier.