From what I've heard, Boys' State is definitely a plus to have on your app. It shows the academies leadership, etc... I'm not sure where I found the statistics, but a significant portion of the Class of 2013 participated in Boys' State (9%?) I'm not entirely sure, but make it known that you did Boys' State!
As for the timing, get everything done AS SOON AS YOU CAN! If anyone out there has a password for their candidate number, let me know. I've tried accessing the CIS System, which is where you do your application. Get your nomination papers filled out NOW, and make it known to your senators and congressmen that you are interesting in applying to USNA. Find a way to stand out (in a good way) because there will be a lot of other people that are just as qualified on paper.