In a complete SA block when there's block of impulse from SA node to Atrial syncitium, The ventricles start pumping at AV nodal rhythm but how do the atria then contract?
It's likely that another point starts setting the pace instead of the SA node. More infos about cardiac pacing on Wikipedia
Or maybe different points try to set the pace contemporary, without generating a valid contraction but only electrical activity (such as in atrial fibrillation/AF, a very common disease mostly in elders).
An electrocardiogram could answer the question for the specific patient. If there is completely no atrial activity you'll find no P waves (no atrial activity) or baseline continuous little waves (in case of AF because of the irregular atrial activity) and probably bradycardia (because the pacer in the AV node is slower than the SA node).