Allied nuclear leverage changes the Soviet counterfactual

Would Allied aversion to a mass-casualty land war give the Soviet Union the advantage?

No; the Allies could fight by other means, and their early nuclear monopoly makes a prolonged war especially dangerous for the Soviet Union without guaranteeing its total conquest.

American efforts to avoid a costly invasion of Japan do not prove an unwillingness to fight. The Western Allies could choose different methods, including nuclear weapons developed years before the Soviet arsenal. Their use against the Soviet Union is presented as an ugly possibility, without endorsement. The likely outcome is a defeat imposed on the Soviet state more like Russia's First World War settlement than a complete conquest of its territory.