Without an inbuilt oiler, does this cause overheating and motor failure? Thus, should one manually oil the chain and bar while in use?

Not according to its manual. There is no reservoir, so says the manual. It says oil the chain each time you take it out to use it.

Yes. And no, the CMCCS320 chainsaw typically has an automatic chain oiling system, so you should not manually oil the chain and bar while in use. The saw is designed to lubricate the chain and bar using oil from its reservoir.