Yes. They can be prosecuted.
If the New York Times told a columnist for the Wall Street Journal that they were going to publish his column and not pay him, they could publish it. It would be impossible to stop them. But, after the fact, the wronged columnist could sue the New York Times -- and win.
It's not "prior restraint" -- the New York Times can't be told not to publish, but they can be held accountable for what they do publish. In the case of the columnist, they can be sued. In the case of treason, they can be arrested, tried, and put to death. The right to publish is just that: the right to publish. Nothing more.
The New York Times can't publish copyrighted material without legal consequences and they can't publish national security information without legal consequences. They are not above the law.
Depends. There is the little matter of the tension between guts and entrenched power.