It would have happened anyway, probably faster, more extensively and without any mass starvation. In 1914 Russia was the fourth largest industrialised economy in the world and its growth rate was so high it would have doubled in size inside of thirty years, and that was under the Tsar’s government that everyone likes to pretend were incompetent and corrupt, not under the Provisional Government that introduced extensive reforms before being toppled by the Bolshevik Coup.
Figures below from The Rise and Fall of The Great Powers.
Russia is a distant fourth in 1914 compared to the top three powers (the US, Great Britain, Germany in order of strongest to weakest). Germany is picked for comparison to Russian growth, I can provide the book's information on the other two if desired (and if such extensive quoting is permitted by site rules).
Let's start with steel production (or pig-iron in 1890).
1890: 2.2. million tons
1910: 3.5 million tons
1913: 4.8 million tons.
1920 OTL: 0.16 million.
1930 OTL: 5.7 million.
1938 OTL: 18 million tons.
To put this in perspective, Germany went from 4.1 million tons of pig iron to 6.3 million tons of steel (1900), then 17.6 to 7.6 (1920), to 11.3, to 23.2 tons of steel.
Energy consumption from modern fuels in the equivalent of millions of metric tons of coal:
1890: 10.9
1900: 20
1910: 41
1913: 54
1920 OTL: 14.3
1930 OTL: 65
1938 OTL: 177
Germany: 71, 112, 187, 159, 177, 228.
Total Industrial potential (UK in 1900=100)
1880: 24.5
1900: 47.5
1913: 76.6
1928 OTL: 72
1938 OTL: 152
Again, with Germany for comparison's sake: 27.4, to 71.2, to 137.7 in 1913, then 158 in 1928 and 214 in 1938.
So, while I don't know how the Soviets would have compared to then nontsarist alternative, Russia's pre-Soviet growth does not indicate it would grow faster under the incompetent and corrupt tsarist regime or something similarly not-really-that-swift.
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