Yes, Olympic athletes can raise a country's spirits for an extended period of time. If an Olympic athlete performs well, he or she can boost a country's national pride, which can then have an effect on the people of the country working together for an extended period of time, as long as that national pride is fostered.
Michael Phelps is the perennial American sweetheart whenever the Summer Olympic Games come around every four years. When it is not Olympic season, however, he keeps a lower profile. Olympians can inspire their home country's a great deal, but keep that going they must stay in the spotlight and highlight issues important to them.
People forget about the games after a few days, so I don't think spirits of the people can be raised very long. Reality sinks back into people's lives and they forget the victories of a few days ago. Of course it raises the spirits of the winners for perhaps a lifetime.
Despite the drama and hoopla of something tied so closely to national pride, it is my opinion that Olympic athletes are simply not enough to boost a country's spirits for any length of time lasting longer than the Olympic games themselves. For 2-3 weeks, we see a nation rally around a few select people with inspiring physical abilities. However once the games come to an end, the country soon forgets about the otherwise ordinary people, doing otherwise ordinary things (or so it is assumed) for the next four years. Meanwhile, a country in turmoil, such as India, may have myriad problems that citizens must face every day, and face them without glamour, or flash, or any pride whatsoever. Citizens realize that, while being exciting to watch and support, Olympic athletes are not truly representatives of courage nor determination for any challenge based in reality. Life proceeds beyond the games, and as their excitement fades, so then does a country's cumulative spirit.