Not disagreeing with this, but some syncope (fancy doctor name for fainting or passing out) - not all - can be caused by bradycardia, usually in what is known as a "Stokes Adams" attack which is much more than simple sinus bradycardia that's been discussed in this thread - it's due to a blockage in the heart's electrical conduction system. Occasionally, "vasovagal" syncope is caused by bradycardia and low blood pressure caused by excessive output from the vagal nerve - this is the cause of syncope from seeing blood or having blood drawn in some people but again, not related to the stable type of bradycardia discussed previously in this thread.
Uncomplicated, stable, sinus bradycardia usually DOES NOT cause syncope or drowsiness, or any other symptoms.