No, it won't. But there are more important questions you should be asking yourself:
1) Is that extra week going to make a substantial difference in your MCAT preparation and, ultimately, your score?
2) You won't be receiving your score until October either way, so your application will be considered a little late. Are you comfortable with this?
If you're currently considering pushing the MCAT, am I off assuming you are not as far along in your studies as you'd like or you're not achieving the practice scores you want? You can always push to take the MCAT in Jan 2018 or early-spring, be prepared to score as well as you can AND apply very early.
Are you applying this cycle? I recommend doing everything you can to avoid submitting late! There's stigma associated with being a reapplicant (at some, but not all schools), and if I could do everything again, I would probably have waited a cycle before applying. Have you been doing really well on your practice scores? If you get above the 95th percentile, then I think it's a different story and you can probably apply later still potentially have a good cycle.