During the early years yes. Though this was likely as much to do with the fact that Russia was undergoing industrialization and urbanization in these years, which is a stage of development that has produced housing shortages in almost every country that has undergone it.
Also there is the fact that much of the urban West had been destroyed in the incredibly brutal fighting of WWI, the Russian Civil War and WWII which left as many as 7 million unhoused orphans alone. With these considerations it's not as easy to ascribe the lack of housing to the Soviet political economy. Remember, the Soviet Union didn't get a Marshall plan like Europe.
The housing projects under the post Stalin premiers eventually mitigated much of the problem but there appear to have been chronically homeless still that were largely jailed (an outcome ironically similar to what we see in the U.S.).
The solution is always to invent new system, we as a human race must be continually experimenting with our systems. For example, look at Singapore's model for housing.
Having the have it alls at gunpoint, forced to demonstrate the systems fitness & benefits to the citizens or perish. Which is why there needs to be a elphant graveyard clause in tax-law, that destroys all monopolies via taxation.
excuse me, what? they got their housing under control just as soon as they were able to modernize their agriculture-based economy into a modern industrial workforce in less than 50 years