If the Volunteer Army took Tsaritsyn in the Spring of 1918, they would have faced a major quandary: hold the city until Kolchak's forces link up with them, or rush up the river to seize more territory and badger the Red Army further? Whatever choice they make is going to have major consequences.
Hold Tsaritsyn: It would mean that the Whites will most likely hold onto all land east of the Volga for the rest of the war, but the Reds would dig into Central Russia around Moscow and become very hard to dislodge. In OTL the Whites assumed the peasants would revolt against the Bolsheviks' harsh treatment within a year, but the opposite happened, the Communist government became heavily entrenched by 1919-20. In the long term this would lead to a partition of the old Russian Empire, with the Whites capturing much of the territory. The Red Army will lose even more territory to Poland because its resources are going to be heavily stretched. Pilsudsky will not be taking Petrograd or Moscow however, he never had any intention of taking more than the Ukraine and Belarus, so the Whites can potentially use that to their advantage if they can swallow their disgust at losing so much territory to a nation they consider a prime threat to the unity of their state.
Push forward: The Volunteer Army would start a push towards Moscow thinking they can end the war early. A lot could wrong, and my gut tells me they will get into trouble much as they did in OTL. They would get pushed back towards the Volga after a few months, ending up in a stalemate, but far weaker than the other scenario.
As an aside, you friend is more or less right. You should know Volzhsky is a small town during this period, with a population of less than 10,000. Whoever ends up retreating there is not going to find a lot to help them. Any Red Army forces that get trapped behind the Volga after a major defeat in Tsaritsyn are in a lot of trouble unless they go guerrilla.
Hold Tsaritsyn: It would mean that the Whites will most likely hold onto all land east of the Volga for the rest of the war, but the Reds would dig into Central Russia around Moscow and become very hard to dislodge. In OTL the Whites assumed the peasants would revolt against the Bolsheviks' harsh treatment within a year, but the opposite happened, the Communist government became heavily entrenched by 1919-20. In the long term this would lead to a partition of the old Russian Empire, with the Whites capturing much of the territory. The Red Army will lose even more territory to Poland because its resources are going to be heavily stretched. Pilsudsky will not be taking Petrograd or Moscow however, he never had any intention of taking more than the Ukraine and Belarus, so the Whites can potentially use that to their advantage if they can swallow their disgust at losing so much territory to a nation they consider a prime threat to the unity of their state.
Push forward: The Volunteer Army would start a push towards Moscow thinking they can end the war early. A lot could wrong, and my gut tells me they will get into trouble much as they did in OTL. They would get pushed back towards the Volga after a few months, ending up in a stalemate, but far weaker than the other scenario.
As an aside, you friend is more or less right. You should know Volzhsky is a small town during this period, with a population of less than 10,000. Whoever ends up retreating there is not going to find a lot to help them. Any Red Army forces that get trapped behind the Volga after a major defeat in Tsaritsyn are in a lot of trouble unless they go guerrilla.