No, a man first had to be recommended for commissioning by his immediate superior. Then there was an administrative procedure that had to be followed, which ultimately included approval by the President, with the consent of the Senate (this latter step being a formality in actual practice). Also, a new officer was required to pass an examination on drill, tactics, etc. Failure to pass the examination board would result in his being returned to the ranks.

Although a West Point style military academy was planned for the Confederate army, the war ended before it could be set up. That was not a problem, though. The South had a number of first-rate military colleges that produced some of the finest officers of the war -- Virginia Military Institute, South Carolina Military College (The Citadel), etc. -- which mitigated the lack of a national military academy.

A naval academy was established for the Confederate navy, however. A fine book has been written on this subject -- Rebel Reefers: The Organization and Midshipmen of the Confederate States Naval Academy, by James Lee Conrad [Da Capo Press, 2003]. Very interesting book.