Are organizations required to confirm health screenings, etc., for volunteers who are not licensed practitioners (nurses, therapists, pharmacists, advance practice nurses, etc.) but are required by law and regulation to have a license, certification, or registration who volunteer during a disaster ?

Any examples are for illustrative purposes only. The requirements that address volunteer practitioners who are not licensed practitioners, but who are required by law and regulation to have a license, certification, or registration are found in the Emergency Management (EM) chapter of the accreditation manual at EM.02.02.15.  

Disaster responsibilities can only be assigned when the organization's Emergency Operations Plan has been activated.  A disaster is an emergency that, due to its complexity, scope, or duration, threatens the organization's capabilities and requires outside assistance to sustain patient care, safety, or security functions.  Here are the minimum requirements:
 

• Obtain a valid, government-issued photo ID (e.g. driver's license, passport) and at least one of the following:
• A current picture identification card from a health care organization that clearly identifies professional designation
• A current license, certification or registration to practice
• Primary source verification of licensure(^^), certification or registration (if required by law/regulation to practice).  NOTE:  Primary source verification of licensure, certification, or registration (if required by law and regulation in order to practice) of volunteer practitioners who are not licensed practitioners occurs as soon as the disaster is under control or within 72 hours from the time the volunteer practitioner presents him- or herself to the hospital, whichever comes first
• Identification indicating that the individual is a member of a Disaster Medical Assistance Team (DMAT), the Medical Reserve Corps (MRC), the Emergency System for Advance Registration of Volunteer Health Professionals (ESAR-VHP), or other recognized state or federal response organization or group.
• Identification indicating that the individual has been granted authority by a government entity to provide patient care, treatment, or services in disaster circumstances
• Confirmation by hospital staff with personal knowledge of the volunteer practitioner's ability to act as a qualified practitioner during a disaster

(^) Organizations that use Joint Commission accreditation for deemed status purposes may use information from another CMS-certified entity's PSV of licensure as long as the documentation includes evidence that licensure was verified via PSV or via a Credentials Verification Organization (CVO). 
During a disaster, the hospital must oversee the performance of each volunteer practitioner who is not a licensed practitioner.  Based on its oversight of each volunteer practitioner, the hospital determines, within 72 hours after the practitioner's arrival, whether assigned disaster responsibilities should continue.

(^^) Licensed practitioner:  An individual who is licensed and qualified to direct or provide care, treatment, and services in accordance with state law and regulation, applicable federal law and regulation, and organizational policy.