Interesting, i just came accross this in the Coronvirus thread. Seems some new research suggests strenuous exercise doesn't impair the immune system.
https://www.sciencedaily.com/releases/2018/04/180420122807.htm
From reading that, it still isn't clear if they are making the distinction between regular exercise and something especially challenging like a race, a hard LR, or killer intervals workout.
From my anecdotal experience I have regular come down with a cold the day after a hard LR. But I also suspect that the cold would be inevitable and the LR just accelerated the timing by a day or so. It is also to realize that if you exercise regularly then you have a stronger immune system, so even if you do suffer from a suppressed immune system for a few hours after a hard workout that may not lower your immune response to below an average person.
Conversely again, if you are right in the midst iof the peak training for a marathon then it is ;t just the hardest workouts but the accumulated stress on the body that comes to play. In this period, if you are really training closer to your limits, your body is working over time to repair muscle damage, strengthen joints, and create adaptations in the heart,lungs, CBS, muscles, veins to lead to more efficient running. It is possible to over train - over training system is a very serious physiological condition that includes suppressed immune response, hormone issue and various mental effects. During peak training you are pushing your body closer to over training syndrome but hopefully keeping clear. SO I would still expect if you are pushing your training super hard then you aren't helping yourself in fighting illness.
Personally, I gave backed down on training for several reasons. Not really a fear COVID19, but in general you can only sustain hard training over shorter periods. I trained hard for 6 months, building volume, adding more speed workouts, pushing LRs. There is now no timeline for another race so it simply woudln't be safe to keep training. Body needs to recover to prevent injuries. You really need that taper + post race recovery period andf then relaxed training period after a period of hard training whether you race or not.
that still means 50-60miles per week for me, but a big change in focus. Much less pounding out 12mile runs on the hard asphalt trying to improve running efficiency to scarp from 2 minuets form my Marathon PR. Just relaxed running on forest trails, putting in some power hikes and hills. Keeping the pace easy. Trying to maximize fun rather than do runs to specifically train some performance aspect.