Are those suffering with chronic migraine also prone to depression?

Yes: Yes, the overlap is significant. When i lived in another state a neurologist and i cross referred depressive patients with migraines very commonly.

Of course!: Chronic/recurrent pain can get anybody down! not only that, it create a cycle. Disturbed sleep worsens migraine triggers and pain, which worsens depression and energy level, which further affects sleep. See if you can avoid some triggers or take some preventives (inderal, amitriptyline, topamax) to reduce headache frequency/intensity/duration. Maybe Cymbalta (duloxetine) would help both depr and pain as well!