I am not a diabetic (although it is in my family)- I sometimes have a low blood sugar/count. I get shaky, sleepy, and weak. So in a way, I guess everyone could suffer from low blood sugar/counts; I think (personally) it depends on the person.
Diabetic people have HIGH blood sugar; diabetes causes a lack of insulin, which metabolizes (uses up) the sugar in your blood. But anyone can have temporary low blood sugar, if for instance they have missed a meal.