If the Alpha is like XIV 1.0 Alpha, it has to run along with the current version of the game. Really on the first alpha there was nothing to do. The only thing that made the alpha last was that we could only play 4 hours every couple of days. (the two first weeks were more like 1hr of gameplay because of crashes).
But then, as soon as the game was a bit more stable, there were just nothing to do in there... Reaching level 20 is really fast. The area was quite limited.