Manchuria would have been Korea's if Balhae or Goguryo became the dominant power.
I think not. Even back in the Korean 3-kingdoms period, Manchuria was not inhabited solely by the Koguryo people. There were others as well, including the Mohe and the Khitans.
(Plus, how many times Manchuria has changed hands until 1945? Not to mention that it directly borders Mongolia. Meanwhile, various Turko-Mongol tribes from the Mongolian steppe have successfully invaded China for many centuries and China has been the most powerful civilization until the modern era; a much smaller Koguryo/Palhae taking on the nomadic invaders better than China? Wishful thinking.)
Another problem I see is just exactly which people 'belong' to the notion of the Koreans? If the Koreans identify themselves as descendents of the Koguryo people, then what about Paekjae and Shilla? What makes Koguryo more 'Korean' than the other two? Based on what facts, if any?
If this sort of reasoning were to be applied to, let's say, modern England, then the English should emphasize their Anglo-Saxon lineage and make claims over parts of Netherlands, Northwestern Germany and Southern Denmark, since there were three Germanic tribes (the Anglos, the Saxons and the Jutes) who had inhabited along these three areas before they jumped to the British Isles. But we do not see the English making such claims.
Therefore, strictly speaking, the (ancient) Koguryo people are not (modern) 'Koreans', just as the (ancient) Germanic tribes are not (modern) 'English'.