Give it a try, doesn't hurt to at least try. If you want to attend the Naval Academy, all you have to do is apply and do the process. But don't have the regret of not trying on your shoulders. Regardless of what anyone says... If you want to attend the Naval Academy or West Point, just give it a good solid go at the application and hope for the best.
You can always apply, but I would recommend applying to west point as well. With a commanders endorsement your chances of getting in are pretty good, but the point is mute if you are dead set on going navy. Also, I wouldn't expect much help from your unit considering it is the navy. If you don't mind me asking, what is it that you want to do as a naval officer?