I believe it is feasible, but accuracy will be much lower then same thing with hedge fund. The key point about hedge fund research is that
For years investors have widely accepted that financial markets are driven by fear and greed
So, if people are afraid, they tend to sell, and if they are greed, they buy. Sentiment analysis just gives data how much people are currently afraid, and how much of them are greed, and thus predict market movements. (This is very rough model, of course, but you should get the idea).
Now about sports. Does fans' mood influence players in sport games? Well, most probably it makes some effect. But is this effect visible at all? I'm not certain about that.
You can also try to find correlation between fans' mood and game results (before the game starts, of course, after the end it makes no sense for prediction), but most probably it will be very similar to what bookmakers tell you.
Note, however, that I'm not sports fan, so I may miss some trends, that you are familiar with :)