I see no harm in your DS reaching out the coordinator to confirm that the file is complete, and ask if anything is needed but the fact that the file has been sent on is I believe validation it's completed and now just being processed. Just for peace of mind though, he can g'head and call.
The reality is as you stated though - until you're out of the competition for a scholarship, you're in it - so he still has a shot. I remember my DS's NROTC application sat in "no decision has been made on your application" status for months - while Army and Air Force had awarded him 4 year scholarships more swiftly. Ultimately, he was offered a scholarship for the Navy too, accepted it, and will commission as an Ensign in a few weeks then head to Pensacola for flight school eventually.
Hang in there- he may be in this state for a few more weeks - If I recall a bunch of people heard their decisions in mid-April, and a few more after that. This scholarship is competitive so I would also recommend lining up plans B, C, D just in case this scholarship does not come through. He should keep himself physically, mentally fit and prepare with a good nutrition, sleep plan too as if it works out, he might be off to NSI summer indoc training just a few weeks after receiving this scholarship. Some of those plans can include joining ROTC in college as a college programmer and competing there for the scholarship if it does not happen out of HS. Good luck to you and your son, and thank you for his willingness to serve.