i don't exercise while ill with the exception of my full-time job with children, raising my own kids, and housewifely jobs around our home
with my body, if i stress it out farther with exercise during an illness (even in the recovery time of antibiotics) it will turn into something else...for example, a mild cold will rapidly turn into pneumonia, which has landed me in the emergency room before....that particular time, i thought "oh i'll just boost my body with a light jog" and went jogging while having a cold...it went downhill from there and ended up not being able to hardly breathe within a week...my DH MADE me to go the ER and my lungs had filled up with fluid
so i know that about my own body...however, others aren't like that...some people's bodies may respond favorably to a little "kick in the butt" while sick or recovering...i'm sure others will chime in with different experiences
but that's my experience and how i learned that exercise while sick is just not a great idea for my own body