Let's say for whatever reason, the Soviet Union never gains diplomatic recognition from the West (think Taiwan/ROC vs PRC after the communist take over)
Instead, some Russian government in exile is cobbled together and recognized as the de jure successor state to the pre-October Revolution Provisional Government.
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1. How does this effect global geopolitical relations during the Interwar years leading up to WWII?
2. With no major trading partners in the west could the USSR survive?
There are at least four problems with the PRC/ROC analogy:
(1) The ROC was not a government in exile in any strict sense; it actually controlled some territory (Taiwan). Recognizing it (even at the cost of non-recognition of the PRC) was not the same as recognizing a "government" that didn't control anything. If Taiwan had fallen, the PRC would probably gotten recognition from many western countries much earlier than it did. As it was, the Chinese civil war, unlike the Russian one, had not technically ended, so the default position was to continue to recognize the government you already recognized.
(2) Even in OTL, the UK was quick to recognize the PRC, and the Scandinavian countries were quick to follow suit. France did so by 1964, fifteen years after the communist victory--not so different from the US recognizing the USSR in 1933, sixteen years after the Bolsheviks seized power.
(3) Given that anti-Bolsheviks ranged from right-wing monarchists to peasant socialists, it would be practically impossible to get a government-in-exile with sufficiently broad support to impress the western powers (though even a united émigré community probably wouldn't impress them very much).
(4) In any event, by the 1930's, the Great Depression created strong pressure for recognition even among those countries that had not recognized the USSR previously--the (dubious) belief that the "Russian market" would help ease the West's economic problems, and the hope that the USSR would restrain Japanese aggression in the Far East. (Of course there could be some degree of economic interaction--trade and, under the NEP, investment--with the USSR without diplomatic recognition, which is why your "With no major trading partners in the west could the USSR survive?" seems to me to conflate two different issues.)
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