Patri Friedman doesn't think so, and he makes a solid case (in the comments):
"There is a zero-sum nature to sports which is not present in music. The existence of sports may create net positive utility, but is that true of who wins a particular game? There will always be a winner and a loser, why does it matter which is which?"
There are two obvious "net benefits" of sports. The first is that they encourage youngsters to exercise, which decreases stress and whining. The second is that they can sometimes rally a community behind a common goal. Hopefully not to the extent of Green Street Hooligans, but maybe something more like Hoosiers.
But this is avoiding the question. What does it matter if a particular team wins? I think the best example here is to be the World Cup, which I truly want the United States to win. Although in the long-run we would expect for every country to have enough talent and luck to win it once or twice, in the long-run we're all dead. This is especially true of the World Cup, since it is only played once every four years, and there are 135 potentially winners (in 2010).
There is a good chance that the US will never win the World Cup in my lifetime. And since scarcity breeds value, I want the US to win even more. And I know I'm not alone! The Cup is a movie about a bunch of Tibetan Buddhists who come together and watch the 1998 World Cup finals. They support France because the French were sympathetic to the Tibetan cause.
So in the long run sports may be totally zero sum and the benefits to everyone will be equal. But in the short run span of my lifetime, I'll be rooting for the US, and I'll be thinking that sports matter at least a little bit.