It depends. Some migraines can not cause damage to eyes. But some migraines can damage to eyes, and even cause blindness. For example, migraines are caused by trauma or tumor can cause a lot of eye problems. See a doctor if your eye problem is caused by migraines to prevent it from becoming worse.
Till now, i never seen that migraine can cause permanent eye damages. A migraine is usually means an intense headache that occurs at the front or one side of the head. It may also cause other hurt. People with migraine may also experience nausea, increased sensitivity, poor concentration, sweating and abdominal pain etc. If you suffer it, you'd better consult an doctor and treat it immediately.
Yes, it will cause the damage to your eyes because of migraines. As we know, the nerves in the whole body are interlinked. If you have the migraines, your eyes pressure and nerves will be affected. You may have the symptom of dryness of the eyes. You should use some eyes drops to release the symptom of eyes. You could also use the warm compress to make your eyes feel comfortable.