When UN forces crossed into North Korea the UN forces had defeated the North Korean army in the field. The war looked to be almost over at the time. So the natural course would have been to keep moving into North Korean territory.
At the time Chinese government officials were warning diplomates that they would intervene if UN forces went into North Korea. these statements from China were not believed in the West.
The answer is yes. Un forces should have gone into North Korea and as they moved to capture more territory opened negotiations to end the fighting. UN commander Douglas MacArthur did not believe that the Chinese would intervene and if they did that the UN forces could defeat them.
