I retook my MCAT at the end of July (7/25) this cycle, so I did not get my score back until late August. It was fine to me and I was still able to get accepted. Though I took my MCAT in late July, I submitted my AMCAs mid June and indicated that I will be retaking the MCAT in July. My AMCAS was verified in a month and I received most schools' secondaries a week before my MCAT date. Only a few schools said that they wish to wait until my scores comes in to send me a secondary, but it was fine because I used that time to work on the other secondaries anyways. (I am also from CA and only UC Davis said that they will wait for my MCAT). So you're fine, pushing it back to make sure you're ready won't affect your application. As DoctorWhoo mentioned, you may have a hard time selecting what schools you apply too (like I did) since you don't know your score yet, so you just have to be extra careful when researching for schools.
And yes, to your previous questions. I believed the first month or so is just for AMCAS submissions. The first day this last cycle that AMCAS release your verified applications to medical schools was I think June 27 (or somewhere around there). So you'll be fine for sure even if your scores comes in a few days after the first release date. Good luck on the final push of your study!