Given that the only way to solve the problem prior to Turn A was for the colonies to physically flee the Solar System, I'm going to go ahead and guess that opening the Box was a resounding failure. The Earth Federation exists well into Victory, whereas Zeon has vanished and all successors are doomed to defeat and failure.
Zeon is gone but the Federation is a shadow of its former self too. IIRC, by Victory, it only has control over the moon and Side 1. They even had to ditch the Earth more or less because of the environmental damage.
In the end, everyone gets a little bit of what they want but mostly not.