Unqualified in this sense is Unqualified Source Materials. Its the source, the supplier, that is unqualified. Not the material per se. And then by definition being an unqualified source you have not audited them and therefore there is no frequency. If you audit them and they are successful then it is not an unqualified source and the frequency is then 3 years, though you have to evaluate annually. And this is why you have to jump through hoops to get compliant material. NCA-3855.5.
A supplier of materials that has a QSC does not need to be audited to comply with ASME III. However, you will not get away with this when audited by people utilizing NQA-1 and Appendix B as criteria. You will need to audit everyone. Even A2LA labs.