The interplay between blood sugar and/or insulin and the immune system is complicated and still not well understood, but there is something to it. Too much, as well as too little, blood sugar can negatively affect your immune system, or at least certain parts of it.

I once read about an experiment on mice genetically bred to have Type I diabetes. A transplant of new islet cells into the pancreas can cure their diabetes, but normally that requires using drugs to suppress the mouse immune system. In this experiment, they spike the blood sugar before the procedure, and the mice accept the new cells and don't reject them, at least for a while. Eventually the immune system reasserts itself and starts attacking the transplanted cells, but that's a remarkable result.

I have heard the statement that for an adult, it only takes less than a teaspoon of sugar to maintain normal blood sugar levels. I don't have any soda cans handy, but 4 grams of sugar is roughly a teaspoon. A can of cola can be...about 9 teaspoons, IIRC. I doubt that many of us normally drink, say, a cup of coffee with 9 teaspoons of sugar in it. Something to think about.

And, knock on wood, haven't been sick yet.