I don't know about that, actually. Caffeine is the active ingredient in (low-power, over-the-counter) migraine medication, because it has anti-inflammatory properties. People who have chronic headaches may be unintentionally self-medicating with caffeine; for them, the caffeine withdrawal period becomes concurrent with their regular headaches returning.
More anecdotally, when I don't drink caffeine (and I do go off it for months at a time), I get headaches on and off, about once per week or so. When I do drink caffeine, though, I literally never get headaches.