Soviet 1939 strength depends on logistics

Would the Allies have lost if they had gone to war with the Soviet Union over Poland?

Not automatically; Allied combined arms and logistics, together with the loss of external Soviet supply routes, would radically change the 1939 balance.

The Allies would not inevitably lose a war against the Soviet Union if the scenario begins in 1939. Allied artillery, armor, air power, and logistics offered alternatives to a purely attritional land campaign, while a Soviet advance into Europe would remain heavily dependent on rail. War with the Western Allies would also remove Arctic, Persian, and Siberian supply routes, including specialist oils and lubricants that later sustained Soviet operations against Germany. An Allied victory in the resulting three-way conflict appears plausible, although the fighting would devastate Soviet and German territory and would not require total conquest of the Soviet state.