Many singers I know (including me) can actually enjoying singing while they're sick. Even though talking is nearly impossible through all the sniffling, sneezing, and other unpleasantries, something about singing itself seems to sometimes help. Maybe it's all that extra deep breathing, or just taking your mind off your misery for a little while.
Another interesting effect is that sometimes you can access a different sound or lower notes when you're under the weather. If I can muster up the energy, I tend to sing the blues -- for more reasons than I'm feeling bad. It's certainly not a cure for your sickness -- but it can sure lift your spirits for a while.