I’m a nursing student and I love this question - I would not do it myself because I think during illness recovery you’re better off giving your body the “easier” forms of energy, e.g. blood glucose from regular meals. I’ve been told that when people get very sick from something like the flu, the lack of appetite that comes with it can impede recovery. If you’re otherwise healthy and end up fasting during a flu, though, I doubt you’ll really hurt yourself. But you’re probably just better off eating the best food you can until you feel better.