The common features of a psychopath and sociopath lie in their shared diagnosis: antisocial personality disorder. The DSM-5 defines antisocial personality as someone having three or more of the following traits:
- Regularly breaks or flouts the law
- Constantly lies and deceives others
- Is impulsive and doesn’t plan ahead
- Can be prone to fighting and aggressiveness
- Has little regard for the safety of others
- Irresponsible, can’t meet financial obligations
- Doesn’t feel remorse or guilt
In both cases, some signs or symptoms are nearly always present before age 15. By the time a person is an adult, they are well on their way to becoming a psychopath or sociopath.
I would say that your description of a narcissist doesn't match three or more of those traits, so the answer is no. I'm not a psychologist, so don't take my word for it.