I have to agree with Jon, if you're sick, and contagious, it's really inconsiderate to put yourself out among the herd, you're just spreading the joy.
IMO, it's just plain silly to work out when you're sick. You get a piss-poor workout, and you're stressing your body when it's already stressed. Better to take a day or two off, you'll shake the bug WAY faster than if you push through it.
As for supplements, the only thing I've ever found that really seemed to help when a bug is coming on is elderberry, I've never had much luck with echinacea. I think eating clean, having a balanced diet, taking a good multivitamin, staying away from refined carbs and staying well hydrated goes a long way toward prevention of illness to begin with.