Southern Cross is crap. You won't lose anything by skipping it.
Here are two spoilers, the first of which is the only thing SC contributed to the franchise (even crossing over to the Macross series), and the second of which is what you need to know before watching the Invid Saga.
HIGHLIGHT TO READ:
Here's 1: Louie invents the Pupil Pistol, which enables the mecha to achieve target lock just by the pilot focusing on the object. This is used, if not directly referenced, multiple times, IIRC, in both Macross Frontier and Robotech: Shadow Chronicles.
And here's 2: The Robotech Masters fail to prevent the Flower of Life (Protoculture) from blooming and spreading it's funky spores/pollen across the universe and leading their mortal enemies, the Invid, to Earth. And it's all thanks to Dana and the rest of her idiot team. The Invid Saga opens with the Earth already having been invaded and mostly conquered, awaiting help from Admiral Rick Hunter and the SDF-whatever.
(That's all)