What are the effects of someone on dialysis drinking soft drinks without sugar?

Excess fluid. It is not the sugar, unless the person is also a diabetic, but the amount of fluid. Those on dialysis are restricted fluid intake. There are other dietary restrictions.
Depends. If you are on dialysis, the less sugar in the diet, the better. However certain soft drinks like dark sodas (coke, pepsi) have a high concerntraion of phosphorus. Dialysis patients must avoid high phosphorus foods or these levels will lead to calcifications and bone disease.