The answer is no. Leo Tolstoy was considered part of the Soviet canon for novels along with other classical Russian writers like Pushkin and Chekov. Tolstoy had the advantage of not only being banned or censored by the tsarist government, but also was a pioneer in realism as a genre which meant that Soviet cultural authorities painted him as a pioneer for the state-supported genre of socialist realism. The 1979 Great Soviet Encyclopedia entry on Leo Tolstoy concluded that

Tolstoy’s realism was nourished by Russian national traditions, which it in turn helped reinforce, but it has a universal scope as well. His realism had a strong influence on early Soviet literature, and to this day has constituted for Soviet writers one of the most important and vital aspects of the Russian literary heritage.

Although the state sponsored the classics of Russian literature, there is also considerable evidence that there was a popular push from below to read these novels and poets, especially during the Stalinist era. During the mass literacy campaigns a particular Russian word came into being: kul'turnost'. While it translates into "cultured" it emerged with multiple layers and positive meanings about a person's bearing and attitude (one colleague of mine described the closest analogue in English is "a gentlemen and a scholar"). For many Soviet citizens, having read Tolstoy was considered a sign of an educated person and a personal accomplishment.

Sources

Bartlett, Rosamund. Tolstoy: A Russian Life. Boston [Mass.]: Houghton Mifflin Harcourt, 2011.

Fitzpatrick, Sheila, editor. Stalinism New Directions. London: Routledge, 1999.

Lakshin, V. Ia. "Tolstoy, Leo." Entry in The Great Soviet Encyclopedia 1979 Edition, Accessed: http://encyclopedia2.thefreedictionary.com/leo+tolstoy