No, not all narcissists are physically abusive, and in my experience, a large percentage of narcissistic abuse survivors were not physically abused. This is one of the reasons they suffered in silence. The wounds are internal.
Most narcissists use emotional and psychological abuse along with intimidation to control their victims. While many were never physically abused, others say physical abuse did not happen for 5, 10, or more years into the relationship. This can happen because the victim starts to speak up or fight back, the abuser’s love bombing is not working and they feel they are about to lose complete control over their victim, there is some type of stressor that is more than they normally would experience, or there is a change in the victims behavior to the abuse and it’s not affecting them to the extent the abuser desires.
And according to some experts, there are narcissists on the lower end of the spectrum that are not abusive. While not all emotional abusers use physical abuse, most physical abusers use emotional abuse.