Looks like I'm too late to do the OP any good, but for others out there with a similar question, what little evidence exists suggests that exercising when moderately ill does NOT delay the healing process. You might not perform as well as you do when healthy, but you probably don't need to worry about it setting you back.
There are, of course, plenty of caveats around this. "Moderately" ill roughly equates to the common cold. No work seems to have been done around pneumonia or true influenza or the like. And the exercise in the studies has been likewise "moderate", not race effort. And it looks like most folks in the studies were runners, though some work has included cyclists.
Personally, I wouldn't race when feeling crap, due to a worry that slightly off reflexes would heighten the chance of crashing weighed against no chance of performing well. But I don't stop training, and neither do any of the sports med folks that I know.
- Kaminsky, LA. The effect of exercise training on the severity and duration of a viral upper respiratory illness. Med Sci Sports Exerc.
34 college kids exercised at 70% of "reserve" HR (running or cycling), 16 didn't exercise, all were tested pre- and post- infection with rhinovirus (one of the most common "common cold" viruses"); no difference in time to recovery or symptom burden between the exercisers and non-exercisers.
- Kaminsky, LA. Effect of a rhinovirus-caused upper respiratory illness on pulmonary function test and exercise responses. Med Sci Sports Exerc.
45 college kids were infected with rhinovirus, 10 weren’t, all were exercised; no difference in lung function or graded treadmill exercise tests between the sick and non-sick kids.
- Schurr, T. Effect of exercise on upper respiratory tract infection in sedentary subjects. Br J Sports Med.
22 sedentary college kids with naturally acquired colds were divided into two equal groups, one of which exercised at 70% of reserve HR; no difference in time to recovery or symptoms between exercisers and non-exercisers.