Do lots of people get cough syncope, or is it unusual?

Not uncommon. Violent coughing can trigger cardio-depressive reflexes that can functionally slow the heart rate, but also because of the high pressures in the chest cavity produced by the fits of coughing, impair blood return to the heart. All this can combine to drop th cardiac output and blood pressure, resulting in faintness or overt (but very transient) loss of consciousness.