The start of Robotech: The Next Generation explains what happened when the Invid invaded. The Army of the Southern Cross was apparently wiped out, but was Dana Sterling and the 15th Armored Battalion also wiped out?
Now, there is a recently new movie called Robotech: Love Live Alive (2013) (adaptation of Mospeada Love Live Alive (1983) with some new animation) where you see Dana from the 15th squadron leaving Earth.
Dana heading to a Garfish spaceship to leave Earth.
In the movie Robotech The Shadow Chronicles it's confirmed they actually left with no problems because Louie from the 15th squadron is a secondary character.