First of all, it's Jiang or Chiang, not "Kai chek".
Second of all, I believe the plan, should Busan fall, was to relocate a government-in-exile to Japan. I don't know much about the military situation, maybe Jeju could be held as a military outpost? But it's geographically not able to sustain enough of a population to maintain a modern government-in-exile.
It should be noted that Taiwan itself was an aberration of history. By the end of his abysmal performances in both the Second Sino-Japanese War and the Civil War, the Americans had given up on Jiang and were willing to let Taiwan fall. It probably would've been taken sometime in the early 50s if it weren't for the onset of the Korean War and the sudden political necessity of keeping the RoC alive. "Taiwans" are exceptional and rare throughout history and in normal circumstances the world just recognizes the new government rather than propping up an irrelevant rump state.