I can't speak for everyone here obviously, but I've vaped while having a cold. Let me say that for me vaping max vg is the last thing I want to do while I have a chest cold (which happens a lot less now then when I was smoking, but my S.O. works at a hospital and brings all sorts of diseases home). In my case I make a 80/20 pg/vg menthol juice. Helps clear the junk right up.
Of course this may not work for you if you're pg sensitive, I'm not, however, if I vape a juice with too much vg I get a heavy feeling in my lungs even when I'm perfectly healthy, so I rarely go beyond 40/60 and most often vape 50/50.
Also while you're ill you'll want to INCREASE your water consumption. A vaper should be drinking at least a liter of water a day if sedentary (substantially more if active), a vaper who is ill probably needs more than that to carry away not only the byproducts of metabolizing juice but also the toxins the germ are creating.