This is ahistorical. The only "censorship," they faced before they were granted power were in response to an attempted coup. They were radicalized prior to any censorship.

There's just something that doesn't sit right with me about indicating that censorship lead to a radicalization of Nazis. Violent anti-Semitism has eternally been a problem in Europe and both Austrian and German nationalist parties were entrenched in such conspiracy. It was always a violent movement.