So the award itself probably doesn't mean anything. I guess the associated publicity might lead a few more people to watch the film.
However, I could see some kind of immunity from prosecution granted to get him out of Russia, and to confirm what documents were released, happening in a somewhat more marginal change (maybe at the next Presidential transition, but probably not). This would be lesser, because it wouldn't be saying "what you did was right", just that it's in the national interest to end the whole affair.
Nixon was pardoned without conviction.
http://www.nytimes.com/1988/01/05/opinion/l-constitution-all...
Also, I think Triumph of the Will played a huge part in helping Hitler come to power. And in the US, The Birth of a Nation helped the KKK explode in popularity. These aren't particularly uplifting examples, but I think it's clear that a popular movie can have a huge effect on the political landscape.
The film is great, incidentally.
http://en.wikipedia.org/wiki/Bernie_Tiede http://en.wikipedia.org/wiki/Bernie_(2011_film)
This movie was a catalyst in national conversation about nuclear proliferation, and there's evidence that its impact included President Reagan.
It was also broadcast on prime time in an era when that meant a greater number of simultaneous viewers, of course.
The idea that Snowden must first be found guilty in order to be pardoned is simply false, the pardon power is plenary and has no such restriction.