Yes, it is possible to get bulging eyes from iodine deficiency. Iodine is a trace element, which is needed for thyroid hormone production. Iodine can't be produced by human body, so people have to take iodine in diet. Because people of different area have different dietary habit, so some people from the same region tended to develop iodine deficiency in the past, for example, Great Lakes, Canada, and western U.S.. But it is more common before 1920s. Nowadays people already realized the function of iodine. It helps with thyroid hormone production, which is secreted into blood and transmitted to every part of body. This hormone can help body use energy so that the body can stay warm and every part of body can work and function normally. Typical symptoms of iodine deficiency include cold sensitivity, weight gain, fatigue, depression, constipation. If you leave it with no treatment, goiter and protruding eyes would be resulted. For kids, the deficiency would cause mental retardation. Actually, it is easy to have enough iodine in daily diet. Iodine is rich in milk, yoghurt, saltwater fish, cheese, eggs and so on.