I don’t doubt Churchill would recognize Obama for what he is. I do, however, doubt that he would engage in conspiracy theories.
Is it a ‘conspiracy theory’ to notice that he is “untouchable” and basically has the Chinese [idea of] “Mandate of Heaven” despite that America isn’t China?
Churchill was certainly well aware of conspiracies throughout history: not only did he write about them in his histories, his own family was involved in (and also fought against) many conspiracies throughout English history. Catholics versus Protestants, succession struggles, Jacobitism, and a host of other factional infighting and secretly ganging up on common rivals are all part and parcel of English history.
Indeed, the English still publicly mark Guy Fawkes Night, one of the more interesting conspiracies of all time.