Yes, they can; it is even recommended as part of a healthy diet. Dietary recommendations for diabetic patients are the same as those for the general population, and include starchy carbohydrate food as an important part of the diet. This is exactly what bread is: a food rich in complex carbohydrates. Just like for the general population, it is recommended for diabetic patients to eat wholegrain breads. However, diabetic patients must control the amount of carbohydrates they consume per meal more closely, which is why the portion size is key for them.