I was Army, don't know if that changes any of the circumstances.
Since everything is already sent out, go for it. I don't remember the exact process for it, but I think all it took was the battalion commander for the recruiter signing a memo. I want to say about a 2-3 weeks turn around time. You can start talking to a recruiter and get the ball rolling on all the paperwork. Waiting for an acceptance before you submit everything to the board might be a smart move, just to maximize your chances.