I think weed may make me feel better for a short period after smoking, but this comes at the expense of feeling even worse than originally after the come-down. And that's not even the worst of it. The worst is waking up and tasting a mixture of weed smoke, blood, and mucous throughout my throat that's dry as a desert, and sore as shit.
It should be pretty obvious that smoking ANYTHING while sick is a bad idea, simply because the smoke contains toxins that are directly contacting the areas affected by the 'bug' (throat, lungs, sinuses), which just adds to the inflammation and the overall 'battle'. However, it is my belief that even if 'smoke' were avoided by eating the weed or vaping it, it's still not a good idea: There is evidence that Cannabinoids inherently suppress the immune system, regardless of how they are consumed.