Yes and no--but a little bit more no than yes. The biggest international sports event, the Olympics, have often revealed high tension between countries.
In 1936, many American and international leaders tried to organize a boycott of that year's Olympics, to be held in Nazi-ruled Germany. One of the important policies of the Olympics is that the teams can't discriminate on the basis of race or religion--a rule that Nazi Germany was obviously breaking. Unfortunately for boycott supporters, Avery Brundage, the president of the International Olympic Committee, was fairly anti-Semitic himself, and faught hard against a boycott. (you can read more about that on the US Holocaust Memorial Museum website http://www.ushmm.org/wlc/en/article.php?ModuleId=10007087).
In 1976, most of Africa boycotted the Olympics to protest New Zealand's having broken the unspoken agreement among a lot of teams to avoid playing with South Africa while South Africa continued to oppress its black citizens under apartheid (that's about 15 years before Invictus, if you've seen that movie!)
1980 (Moscow) and 1984 (L.A.), the US and the USSR, respectively, boycotted each other's Olympics.
This year, there were some problems with the Lebanese judo team refusing to train alongside the Israeli team. They made the olympic event coordinators put up a division through half the space so that they could train separately. You can read more about that in a Telegraph (UK newspaper) article here http://www.telegraph.co.uk/sport/olympics/judo/9433680/London-2012-Olympics-Lebanon-judo-team-refuse-to-train-alongside-Israel.html
On the other hand, North and South Korea have been at war for sixty years, and they regularly compete against each other without incident. And the fundamentals of the Olympics are peaceful and noble--in ancient Greece, warring city-states were required to adhere to a ceasefire (a temporary peace, called ekecheiria) for the duration of the Games, so that athletes could travel and compete safely.