Would Churchill in Canada have just been a refugee?
Churchill still would have had a lot of power as the leading politician in the British Empire. He may have even held more power in Canada than the Canadian PM, even in exile, provided Britain wasn’t occupied very long. However, if it were I do believe the Americans would have made peace with the Germans. With German control of Europe (East and West), and assumed control of the Ocean it would have made an invasion of Europe impossible, even with the Nuclear Bomb as they wouldn’t be able to fly it there. The odds of Germany winning on all fronts and controlling the sea though were pretty slim, you can’t go to war with the entire world and expect to win.