I suspect that the answer is "it depends on the culture". China seems to have a lot more control over the spread of anti-CCP ideas than Iran has over the spread of anti-regime ideas, and it isn't because of Iranian censors trying less or having worse tools. But the Iranian population seems to be much less conforming and more ready to rebel.
It's still somewhat effective in Iran, it's just not sufficiently effective to prevent protests.
The US has a number of natural experiments that show that censorship is effective at silencing someone. Look at what happened to Trump and Alex Jones after they were deplatformed. Their reach was cut a lot and that wasn't even state censorship.
Russia had a natural experiment after Gorbachev lifted speech codes. People described the renaissance of new ideas being spoken that were previously stifled. Censorship worked.
It makes sense that it works given our understanding of social contagion. People aren't designed to believe facts. They're designed to join a team and believe whatever stuff their team believes in. Things like taboos or censorship or blacklists are effective, however repellent they may be.
You're talking about whether censorship is a good idea.
Separate discussion.