Yes, it is possible to detect diabetes from an eye exam. This because diabetes also affect our eyes and associated with some eye problems. In common cases, the eye doctor will suggest you to see your GP and have some blood tests if you S/he thought you have diabetes. So, don't worry about it. No news is good news. After the eye exam, you will have better knowledge to your eyes.
Yes, this is possible. Eye doctors can directly observe your blood vessels to find out if you have any vascular diseases. And diabetes is just one kind of vascular diseases, you should know this. It is common that diabetes can usually cause some vision problems such as blurry vision, eye twitching and so on. You need to be cautious when you have such symptoms above.