The short reply is "Yes".
The rest of the story is in your "written practice" which describes the details of your emplyer's qualification and certification program for NDT personnel. The job description of each level of certification would describe the scope of work and responsibilities of the Level I, Level II, and Level III personnel.
In-house certification of Level III personnel (as well as Level I and II) would be in accordance with ASNT's Recommended Practice SNT-TC-1A which would be the basis or your company's written practice.
Best regards - Al .