If you make <~501 yes likely, as applying early as possible can help with weaker apps and lower scores won't make cutoffs that often increase around August'ish time-frame.
IF you make a competitive score and don't drag around at all in any other step, then No! It won't help it for sure, but it shouldn't hurt at a majority of schools.
The majority of DO applications come in toward mid to end of July through Sept and DO schools do a ton of interviewing in Sept-December. DO students don't have to put down deposits to hold seats until mid December, so things don't start to solidify until closer to December. From what I saw at my university those not getting any love from MD schools often don't freak out and start the DO process until around November-January. You don't want to drag around and get stuck competing with MD reject students who have a 3.65 and 509 MCAT. So October is on the edge, but with a strong application and MCAT score you still have a reasonable chance with most programs. Just get everything ready and make sure you submit a solid October application. A bigger mistake is applying before you are ready and bombing the MCAT! A 495 even in June often means you'll be applying next year.
Perhaps it's my limited perspective of a few years (and maybe related to changes) but I have seen DO schools appear to fill classes sooner this year than last and every year the scores increase.