The password sync agent that you mention is suited to Active Directory mastered users only. ie whenever an AD password reset or change is made natively, it is sent to Okta. If an Okta mastered user changes their password via Okta user settings page or self-service password reset then it will be done directly against Okta rather than the password sync agent.
No if the user is Okta mastered then the password is owned by Okta and Okta can only write updates down to the AD. The password sync agent is only for AD mastered users where AD own's the password and pushes it (optionally) back up to Okta.