Is it possible that dentures can provoke sinus pain?

Not usually: If not fitted correctly, dentures can cause gingival ulcerations. A simple adjustment usually fixes the issue. Then again, without knowing your situation, maybe the denture is impinging on a nerve which is referring pain to your sinuses. See your dentist for further advice.

Examination: Your Dentist would have to evaluate the fit of your dentures, but it would be highly unusual. Higher probability is that you have a sinus issue, such as infection. See your Dentist to check your dentures. See your Physician to examine your sinuses.