Possibly. If you have significant sinus congestion where you are unable to breathe well through your nose, then you would be a mouth-breather, which will lead to dry mouth. See your internist (md) or otolaryngologist (ear, nose & throat md) to evaluate your sinus problem and determine a beneficial solution.
Dry Mouth and Sinus. If you take antihistamines to help control your sinsus problems that can certainly cause a dry mouth. Also, those with sinus issues often breath through their mouth more since their nose tends to be blocked and that can also lead to a dry mouth. Drink plenty of fluids to keep your mouth hydrated and to help protect your teeth.
Possibly. If you have enough drainage from your sinuses that you find you are breathing thru your mouth, then it may be drying out your mouth.