Dr. Zorba Paster on NPR had a show on this and he said there was a study where one group was given a flu bug and told to take it easy while a second group was given the bug and told to work out daily. It showed there was no difference in recovery rates between the two.

Of course working out is not what most people feel like doing when they are sick. It also doesn't make sense that if you divert energy to muscles it doesn't take that energy away from the fight against the virus but the study says it makes no difference.