The recruiters know if the application made it, we just don't receive an email personally. After the May board the recruiter said he knew that I went to the board, I just never received that confirmation.
There is a phrase that many military families live by; No news, is good news. If the recruiter contacts you now it's probably because something happened and you'd probably be moved to the January board.
Confirmation from your OR is good, from that point forward I wouldn't worry. If they say you're submitted you're probably fine.
At this point there isn't anything you can really do now anyway. All the inquiries about the kit being submitted properly should be done before the cutoff since you'd be risking rolling to the next board if there is an error and you didn't have time to catch it. That's why the admin team exists though, after you're done with all of the edits and adjustments, there shouldn't be anything that gets in the way. The board can cap the number of applicants and if they do that you'll roll to the next board automatically. It's a good thing to try and get it in early for those reasons.