Wrangel was doomed, with or without Polish aid. The Poles simply cannot force the Soviets to agree to this kind of a massive population exchange.
Not necessarily, in the autumn 1920 the Bolsheviks found themselves in a really difficult situation military. Express shortcut campaign in the second half of 1920:
July 1920. - Bolshevik divisions downloaded from all over Russia to the general crackdown on Polish.
Front Belarusian: 110 000 Bolsheviks, 67 000 Poles.
Ukrainian front: 60 000 Bolsheviks, 60 000 Poles.
The defeat in the Battle of the car. The collapse of the front in Belarus. The rapid retreat of Poles to the west. The retreat from the Ukraine.
August - Battle of Warsaw.
Northern Front: 105-140 000 Bolsheviks, 110 000 Poles.
Ukrainian Front: 60 000 Bolsheviks, 30 000 Poles.
Unexpected reversal of the fate of the war. The destruction of the Bolshevik army in the north. The loss of more than 100 000 soldiers.
September - the final victory of the Poles over the Niemen.
October 1920
Belarusian Front: 65 000 Bolsheviks, 80 000 Poles.
Ukrainian front: 50 000 Bolsheviks, 65 000 Poles.
The ratio of guns: 500-800
The ratio of heavy machine guns: 2000-3000
For the first time since the war, Poles gained overwhelming numerical superiority. Losses in equipment incurred by the Bolsheviks near Warsaw were irreversible. Most of the artillery and machine-gun was lost. Losses in the veterans were replenished forced recruitment of random peasants from Belarus. The ratio of forces has changed from 3: 2 in favor of the Bolsheviks to 3: 2 in favor of the Poles. Bolshevik armies were completely demoralized.
In Ukraine, 1st Cavalry Army - the only powerful unit on the front was withdrawn from combat. (Stan war fell from 16 000 to only 5 000 people). On the front line, leaving only the twelfth and fourteenth army, retreating more and more without a fight. In Belarus, Tukhachevsky broke. He was unable even for a few days in Minsk to defend against attack by two divisions. He prepared all of his four armies to retreat deep until the Berezina and the abandonment of Belarus.
In the south of Wrangel, the last white general, he gathered the remnants of Denikin's troops and took the last offensive. In March of 1920. His forces numbered only 3 000 people in a state of battle but in June 1920. Increased to 12 000 people. With surprise, despite the Entente XIII he attacked the army Bolshevik (15 000 people) occupying the southern Ukraine to the Dnieper, and Zaporizhia suburbs of Donetsk. In October, despite the additional download VI Army and Second Cavalry Army, the Bolsheviks were not able to defeat Wrangel. His forces then counted up to 43 000 soldiers against 45 000 Bolsheviks.
Wrangel to connect with the Poles marching east took the last offensive on the right bank of the Dnieper, trying to move in the direction of Kiev. At the front of the Polish Bolsheviks they suffered defeat after defeat. Their armies retreated 200 km a month. Poles were 200 kilometers west of Kiev, Wrangel 300 km to the south-east. To maintain morale broken Tukhachevsky spread rumors that from Siberia to help will arrive V Bolshevik army. In fact, they had quickly available reserves.
Of the 18 Army, 7 fought against the Poles, 3 against Wrangel, one (VII army) remained in the area of St. Petersburg for fear of war with Finland, which has not yet signed a peace 3 armies remained in the North Caucasus to fight the Cossacks, 1 Army (XI army) fought with Armenia, 3 were involved in Siberia.
The Bolsheviks were afraid that in a few weeks the Poles will join Wrangel and consequently surround and crush their army in the Ukraine and then go to Moscow. XIV Army and I and II Cavalry Army threatened to push the border with Romania and total annihilation. They panicked and were ready even to give Poland the borders of pre-partition of 1772 so long truce within 10 days.