Based on most of the answers thus far, I think it safe to say that winning an award is far more beneficial than not for a game or product.
While there are those that ignore awards, or who are not aware of them the number of people who are less likely to look at a game because it has won an award are statistically insignificant when compared to 1) Those who actually want to examine award winners and 2) the positive word of mouth generated by the fact an award has been won. Even those who look at award winners without buying them, I would suggest, play into that second point, helping to generate and maintain the positive word of mouth that will result in more sales.
Or, in other words, a company can only gain from being part of the award process. Its hard to see a downside.