No, V4S Kiosk User need not be a Salesforce User to access V4S Kiosk application.
V4S Kiosk User must be added as Salesforce Contact and should also have a V4S Mobile User record which is marked with "Is Kiosk User", to log in to V4S Kiosk application on the phone.
Only the Salesforce User who needs to have access to V4S Mobile Objects must compulsorily have a Salesforce License. This can be Volunteer Coordinator, Volunteer Manager or Salesforce Administrator who check the Volunteer Reports or Volunteer data in Salesforce.
More information here for creating V4S Kiosk User.