Can I detect talc using HPLC and, if I can, why does it work?

No, talc cannot be detected by HPLC.

Detectors generally used by HPLCs, especially the UV-Vis detector, are for organic functional groups. This means that HPLCs are used for testing organic compounds (most pharmaceutical active ingredients, complex organic components of food, drugs that are organic in nature, etc.).

If you are aiming at positively identifying talc in a sample, it would probably be best if you used an FTIR or an X-ray diffraction method. These two are used in the identification of talc in the USP.