We know this because an almost identical plan was tried by President Bush, and if that plan had worked we wouldn't need this plan.
It's a fact of foreign relations that using PR to persuade foreigners that they're wrong about the U.S. simply never works, and often has the unintended opposite effect of reminding them why they hate us. The specific problem in Pakistan is that U.S. forces -- the CIA in particular -- frequently fly predator drones over Northern Pakistan and use them to kill suspected terrorists. Predictably, innocent people get killed too, and for some strange reason Pakistanis are upset by all this. Will $50 million in advertising make them feel better?
Here's a test. Take a look at this ad for RT News, a startup cable channel here in the U.S.:
Now, once you learn that RT News is funded by the Russian government, and its stated purpose is to persuade Americans to look at "different sides" of the story, are you more or less sympathetic to the idea that Obama is more of a threat than Iran's Ahmadinejad?
The U.S. tried this before under Bush. Charlotte Beers, the former head of ad agencies Ogilvy & Mather and JWT, tried and failed to do the same thing after Sept. 11, 2001. She was replaced by Margaret Tutwiler, James Baker's press secretary during the presidency of Bush senior, who lasted six months before giving up.
If you want a detailed history of U.S. failures in using ads to get Muslims to like us, download this GAO report from 2006. On page 11 it describes how many Muslim TV stations refused to carry the ads because they were from America, and even when Muslims did get to see them they were widely dismissed as propaganda.
The oddest part of the campaign was the Pentagon's brief adoption, and then abandonment, of Saatchi & Saatchi CEO Kevin Roberts' suggestion that the War on Terror be rebranded "the global struggle against violent extremism," in 2005.
So there it is: History shows us two things: First, that America's image abroad is largely a function of its foreign policies and cannot be shaped by advertising; and second, that both Republican and Democrat administrations remain addicted to the idea that the opposite is true.
Photo by Flickr user Jon Person, CC 2.0.