If an Investigator loses Health to become Defeated during a Combat Encounter with a Monster, but the Mythos card revealed in that round, The World Fights Back, allows an Investigator to Recover 2 Health, can that Investigator be healed to continue the game?

Nope. You can find the answer in the Ref Guide, pag. 4, under "Defeated Investigators":

A defeated investigator is not considered an investigator. A defeated investigator cannot perform actions, resolve effects, or be affected by effects that affect investigators.

So, the Mythos card healing investigators triggers an effect that affects investigators. The defeated investigator is not considered an investigator, and he's not influenced by any game effect, as per quoted rule.