It might be different this year with OptomCAS, but previously you were able to apply as early as you wanted, then send your OAT scores in when you get them. I know for a fact that other professional school application systems allow you to do this, so it would make sense that you could do it with the new system.
The response from the schools varies: some will not even look at your file without it being complete, some might give you feedback right away. Best to call the schools you're interested in to find out, but either way I don't think it would HURT to get it in ASAP, assuming everything is in order and you're not rushing it just to have it in on July 15th.
I know that this cycle is going to be a little different, however to ease your nerves, I applied in late August, early September. I didn't take my OAT until late September, meaning that the schools didn't actually get my official scores until a couple weeks after (but I faxed them unofficial copies). However, I was in the first interview date for two of the schools I applied to (and had early invites to the rest), and my GPA isn't mindblowing, I wasn't the president of the world and didn't cure world hunger 😉
Also, something to note is that even though the application system is AVAILABLE July 15th doesn't NECESSARILY mean that the schools will all be immediately reviewing applications starting then. For example, if school XYZ says they're not actually going to start reviewing applications until September 1st, someone who applied July 15th would probably be in the same boat as someone who applied August 15th. Again, best to call the schools to see when they will begin reviewing applications.
