Recovery from illness vs training stress - Any correlation

I have seen little correlation. I'm very good at recovering from training stress. I can do absolutely ridiculous things in training, have little or no soreness and be good to go the next day, esp. if it was  endurance-focused and at moderate intensity rather than a speed workout. But it can take me a long time to get over colds, sinus infections, etc., even if I'm not training at all. In my case I'm pretty sure it's due to allergies and asthma, which just up the level of irritation and keep me feeling lousy for several days (or, when I lived in China, weeks) even after the germs have cleared my system. I think it's just individual and varies with the body system and person. However, if you consistently see slow recovery from both illness and training, it's possible that overtraining (or an underlying issue like anemia or poor diet or sleep) could be suppressing your immune system as well as your performance.

There are a ton of variables common and unique to both processes.  I suspect there's little correlation but I'm totally basing that on an educated guess with no evidence whatsoever.  However now that I think about it, relative to a baseline average fitness and diet, if you improved your fitness and diet significantly, over time I'd bet you'd see improvements in both 'sickness' and exercise recovery times, depending on the illness and existing medical conditions of course.  That's really just a reflection of being healthier.