Good question. Do one or both of your parents have diabetes?
There are a variety of factors that influence diabetes. There are two types, as you most likely know, type 1 and type 2. I'll post a fairly short answer. Genetics and environment influence diabetes. Type 1 diabetes is caused by an autoimmune attack on the pancreas, resulting in inability to produce insulin. Type 2 diabetes is where the body either does not make enough insulin, or it does make enough but the body is unable to use it. This is where insulin resistance occurs. The glucose in your blood stream simply does not respond to your own insulin. Type 1 and type 2 diabetes are dependent upon the genetic predisposition (whether your parents have the disease, either one or both of them), as well as environmental factors such as diet and exercise. For type 1 diabetes, both parents must have the disease for it to be inherited, in most cases. I could go on for days about this disease, it's physiology, etc.
However, to answer your question, yes you could follow the recommended diet. The best thing to do, though, is exercise daily (at least 45 min to an hour), eat tons of veggies, chicken, fish, various nuts, oats, and fruit. So many people with diabetes could be cured early on, simply by exercising and eating properly. Sugar intake is the one thing you need to strongly mediate throughout the day (as everyone should). High sugar, without exercise, will increase fat storage. The higher the body fat percentage, the greater a person's risk for diabetes becomes.
You must not have Type 1 diabetes currently, since the title of your post suggests you have not personally been diagnosed with the disease. So, you are in good shape statistically now, as long as you exercise daily and eat properly. If you start to become fat, you are increasing the probability of the onset of Type 2 diabetes.
Let me make it clear, though, that you will not simply get Type 2 diabetes from eating poorly and becoming obese. The genetic factor must be present as well.
If you have any other questions, feel free to ask! Let me know if any of this was confusing or unclear.