It is possible to have both; some others here do. I do not. I can't imagine teeth grinding or jaw clenching does anything good for CHs, but instead could be a trigger. Blessings. lance

There is a surprising volume of medical literature on the relation of dental issues to CH, much of it rather too complex for us to undertand.

This abstract doesn't directly say, "yea" or "nay" on a relationship but is saying: don't waste your time--refer.

Basically, my years of searching has never turned up medical studies which demonstrate a causal association.

The link that you see between these two conditions is not of one condition causing the second. Rather, there is a complex web of nerves serving our head which can carry pain signals of Cluster to, we regularly experience, our teeth, temple, and eyes. We do not accept that any of these three sites are causing Cluster, however.
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4.J Am Dent Assoc. 2008 Dec;139(12):1616-24.

Trigeminal autonomic cephalalgias: a review and implications for dentistry.
Balasubramaniam R, Klasser GD, Delcanho R.
SourceDepartment of Oral Medicine, University of Pennsylvania, School of Dental Medicine, Philadelphia, USA. ramesh.balasubramaniam@uwa.edu.au

Abstract
BACKGROUND: The authors review the epidemiology, clinical features, pathophysiology, diagnosis, treatment, orofacial presentations and dental implications of trigeminal autonomic cephalalgias (TACs): cluster headache (CH), paroxysmal hemicrania (PH) and short-lasting unilateral neuralgiform headache attacks with conjunctival injection and tearing (SUNCT).

TYPES OF STUDIES REVIEWED: The authors conducted PUBMED searches for the period from 1968 through 2007 using the terms "trigeminal autonomic cephalalgias," "cluster headache," "paroxysmal hemicrania," "short-lasting unilateral neuralgiform headache attacks with conjunctival injection and tearing," "epidemiology," "pathophysiology," "treatment," "oral," "facial" and "dentistry." They gave preference to articles reporting randomized, controlled trials and those published in English-language peer-reviewed journals.

RESULTS: TACs refers to a group of headaches characterized by unilateral head pain, facial pain or both with accompanying autonomic features. Although their pathophysiologies are unclear, CH, PH and SUNCT may be differentiated according to their clinical characteristics. Current treatments for each of the TACs are useful in alleviating the pain, with few refractory cases requiring surgical intervention. Patients with TACs often visit dental offices seeking relief for their pain.

CLINICAL IMPLICATIONS: Although the prevalence of TACs is small, it is important for dentists to recognize the disorder and refer patients to a neurologist. This will avoid the pitfall of administering unnecessary and inappropriate traditional dental treatments in an attempt to alleviate the neurovascular pain.

PMID:19047667[PubMed]