Yes but: IF ( and that's a big IF) Fox allowed him to post on social media, then Fox loses. Twitter is a social media company (for now and at the time of the contract). IF Tucker went on CNN, or MSLSD, or a TV network, he'd be violating the NDA and probably the employment contract. Again, the courts can't fix a bad contract. If Fox didn't specify that Tucker can't do POD casts, or post on social media, then Fox loses.
Simply being terminated DOES NOT violate an employment contract or an NDA. An employment contract contains the terms of employment. They usually have a clause like we will pay you [amount] for [task], however we can terminate you for....morals violations....drug usage...not doing your job...bad ethics....harming corporate moral...putting the company in jeopardy, and a lot of other such clauses. The NDA would survive such justified terminations.
Something that would terminate an NDA would be if the company stopped paying the employee. That's a violation of the contract. The NDA would probably NOT survive a contract violation.
The courts will NOT protect a company for making a bad decision. If the company enters a contract that has bad financial consequences, for example, the court will not save the company from a bad decision. A contract is a contract, good or bad.
The courts have consistently ruled that you can't take someone's lively hood away in an NDA agreement. So for example, you can't order a painter to not paint. That would take away his trade. Fox has moved to the left. Tucker is clearly NOT LEFT. It would be like CNN suing Rush for infringing on their audience. It has been reported that Fox agreed to allow Tucker to have his social media. Well, Fox, you screwed up, bigly. Can't cry now.
It appears that she isn't going to throw out the case.