No, this case has never been overturned. It is not at all likely that the case will be overturned any time soon since the Supreme Court has tended to rule in favor of protecting more kinds of speech, not fewer.
The issue in Cox v. Louisiana was whether states can prevent people from demonstrating peaceably if their demonstration would be likely to cause other people to become violent. In legal circles, this is sometimes known as giving people a “heckler’s veto.” That means that it allows people to prevent a certain kind of speech by reacting violently to it.
We should be clear that the speech in question is not meant to incite violence. It does not consist of someone saying “let’s burn down these buildings.” Instead, it is about people who dislike the message of the speaker reacting violently.
It would be wrong to allow the government to ban such speech. If the government did, anyone who disliked the message of a speech could get it banned by going and starting a riot during that speech. That was what the Court said in Cox. This idea has been reiterated time and again, notably with the recent case about the picketing of soldiers’ funerals by the Westboro Baptist Church. Our laws do not allow us to prohibit unpleasant speech, regardless of how people who disagree with the speech might react to it.