Logically, it would have to take less than a year or so. In the DS9 episode Valiant, the ship of the same name was on this mission before the war broke out:
The Valiant's a state of the art
warship. Our mission was to
circumnavigate the entire
Federation before returning home.
So it couldn't take much longer than that if Alpha Squad cadets were expected to graduate on time and take required classes in four years (or five if the comment about Merik being dropped in his fifth year from "Bread and Circuses" can be take seriously...