Player 0 is right about North Korea's industrial development versus South Korea's, to a point. Prior to the Korean War, the northern part of Korea was not only Korea's industrial heartland, but was one of the industrial powerhouses of the Japanese Empire. That is, until the Soviets occupied the area at the end of WWII and US strategic bombing during the Korean War substantially reduced the remainder. Finally, of course, industrial development in the South had surpassed that in the North by the 1960's or 1970's.
As to whether the U.S. would have invaded Manchuria or not, whether the PRC knew it or not, the U.S. simply had no intention of invading. It was obsessed with the old warning to "avoid engaging in a land war on the mainland of Asia". The US did not even attempt such a thing during WWII (minus a few thousand of Merill's Marauder's in India and Burma, and thence to advisory missions in China), even though their principal ally in the Pacific Theatre, China, was holding down the bulk of Japan's military force. That should speak volumes about what U.S. thinking with regards to fighting in China would entail; clearly they balked at the very notion. That they even intervened in Korea to prevent the fall of the South marked quite a departure in US foreign policy, as prior to the Korean War the US really was adverse to engaging in any major wars short of general war itself. In any case, both the Administration and the Joint Chiefs of Staff were opposed to entering China, and very deliberately adopted the policy of "Limited War"; the Korean War of course was the first time the U.S. had done so, and indeed the policy was invented for the occasion, including the deliberate refraining from the resort to atomic weapons for fear of it provoking a general war with the Soviets. Finally, the US simply lacked the strength to advance beyond the Yalu River, and in the event, did not even possess the strength to hold it against the PVA.
One thing that the PRC leadership did know, or at least firmly believed, was that they could hold the UN Forces well south of the Yalu River at the very least. And of course, the PVA actually attempted to drive the UN Forces deep into the South, if not drive them out of Korea entirely. The PRC would not have dispatched the PVA to war in Korea if it genuinely feared an U.S.-led UN invasion of China; if it had, it would have massed its forces in Manchuria and deployed them for defence in order to receive a militarily superior enemy. That the UN Forces were not militarily superior, or at least not sufficiently such to afford them the ability to invade China, was implicitly understood by the PRC leadership and the PLA. Otherwise, dispatching the PVA to Korea would simply have been tossing good troops to the wolves. In the event, of course, the PVA nearly drove the UN out of Korea in late 1950/early 1951, and the UN proved able - and willing - to only seek to restore something like the original demarcation line between North and South.
