There's no need to be snippy. I pointed out the spelling simply because you were clearly uncertain about it (you've spelled it two different ways in this thread alone), and your snide comment about expertise in galactic politics is completely unnecessary. I'm not sure what you're trying to prove here. There's no need to take that tone of "voice" in what is essentially an inconsequential discussion about an entertainment product.
The Star Control lore establishes that the Kohr-Ah and Kzer-Za were so evenly matched that they were likely to fight themselves to mutual extinction. Only the discovery of the Sa-Matra allowed the Kzer-Za to stop the war before it got to that point.
But don't take my word for it. Here's what the Ultronomicon has to say about the subject: "With both the Kzer-Za and the Kohr-Ah fleets nearly evenly matched, the civil war would likely have resulted in the complete destruction of the entire Ur-Quan race had the Kzer-Za not found a mysterious Precursor warship. This vessel, later called the Sa-Matra, broke the stalemate and ended the decades long war in a matter of days."
And that's the foundation for my claim that the Ur-Quan would have been extinct. Arguing details is a bit silly seeing as we're discussing what-ifs of fictive ancient history. Could the Ur-Quan have survived without the Sa-Matra? Sure, thanks to the wonders of fiction. Anything can happen if it's dramatically appropriate and not entirely unbelievable.