In NC it does not matter. DS had his in about 1 month prior for all MOCs and he got all MOCs noms.
The key is to remember they have somebody in their office that works directly with the nom process. Call the office(in NC it is the in state office ---not DC) and ask them directly does it matter. State to them I have heard that early apps get preference since it shows their dedication. They will be honest and precise. We can only give our own MOC experience.
Do not have the folks call because it does look better that you are taking control and that it is not the folks being the driving force. This will always be concern that the child is doing ths because of Mom and Dad. If the folks call make sure they state a valid reason, that can be verified through your app. i.e., you are a lifeguard that works 9-6 M-F, Football camp, volunteering somewhere away from the home for the summer. That job/camp/volunteerism will show up in your resume, and they get it. However, what I would suggest is if this is the scenario, the folks call and find the direct extension or email, have them give the background questions. Then let the folks pass it to you and you call the moc nom rep leaving your cell phone no on their voice mail for any follow up questions.