No, they wouldn't, it would end up on the cutting room floor and our guys know it. It's going to take a live press conference, with most of the world watching. Even then, with the five second cut off I wouldn't put it past the dishonest journalist to cut them off so it can't be heard.
What they can't cut off though, is 160,000 soldiers all returning home to tell their friends and families. That word will begin traveling fast, and the local papers will print it. The small local papers are the only ones who still have honest people working for them.
What if agroup of returned soldiers, no longer in the service (so they're not breaking any military discipline), did a sit-down hunger-strike in front of the NYT building? In the snow. With Fox News covering it every day. And Rush going there in person to talk to them on the air. And Bush even dropping by to "hear their concerns". Or at least sending Cheney.