Sure it would have, not always perfectly, but close enough especially in an Internet world where smart messaging in any media would have been repeated and forwarded. The problem was that the anti-war messaging was so bad that even most activists didn't want to listen to the podium.
I've always been singularly unimpressed with complaints about the media as the problem just as I'm singularly unimpressed with complaints about lacking money as the cause of progressive failure.
Many of the mass marches in American history have happened with little media support-- the 500,000 Webster march for abortion rights happened in 1989 with no big media pushing it, just lots of networks of women fearing that the Supreme Court was about to overturn Roe v. Wade.
Spanish media may have helped encourage turnout in LA, but the rest of the media was quite willing to promote the message of the organizers that it's wrong to criminalize immigrant workers and those like the Church who help them. It was a clear message backed by mass action and resonated with a large portion of the population, so it projected well into the mainstream media.
The antiwar movement has neither had a consensus message internally nor one that resonated well with the American people, even ones who didn't like the war. When many folks against the war are embarassed by the antiwar rallies, it's hardly shocking that the regular media doesn't cover it well.
Nathan Newman