InDesign keeps its metadata according to the XMP protocol, Extensible Metadata Platform, so yes, you can add custom categories to be stored inside the file for an image — assuming the file format allows this. (In fact, many of the XMP fields are drawn directly from IPTC, suggesting XMP was originally intended for images.) I have never tried ID's automated caption subsystem, so I don't know whether it can be modified to use custom fields.
Adobe's SDK for XMP includes a pre-built custom panel you can modify to input data into your custom fields. I've only used it for IDCS4, where installing a custom panel requires care (i.e., it can be installed on multiple machines, but I wouldn't rely on end-users to do the job). With IDCS5, custom panels can be made as Flash plug-ins — simple to install but requiring more programming skill to make; tomaxxi.com offers one to simplify inputting data in stock XMP categories, as well as several how-to's on XMP.
As collywolly suggests, Bridge may be better suited than ID for modifying metadata, and Adobe has a forum devoted to using scripts to automate processing in Bridge.
Good luck,
David