It would never even occur to me to ride while I'm sick, and I will define "sick" in really high tech medical terms as "feeling bad." I'm home sick right now, and the last thing I want to do is exert myself in any way. I'm on the couch with a book, laptop, and roku so I can watch some Netflix (Eat, Pray, Love this morning. Mostly boring, but part about forgiving yourself really hit home).
I guess it depends on degree of sickness, but it is hard enough to ride (since I don't live in a flat area) when I'm well. I don't need to be making it harder. I will ride when I am feeling well again.
I also know that I am very fortunate that my sickness is temporary and with some medication and time will get better. For those with chronic conditions who don't have the luxury of knowing you will be completely well in a few days, I salute you for having the inner fortitude to get out there even when you do not feel well and are in pain, and I sincerely hope that the exercise does all the good things for you that we hear it does!
Grits
2010 Trek 5.2 Madone WSD, SI Diva Gel Flow
2002 Terry Classic, Terry Liberator