Kay asked: Can I use GIS to map our stacks and create a method for getting from a catalog record to a shelf location?

Answer: Yes! This is a great but atypical use for a GIS! ESRI has some more detail on library type GIS setups here. You can simply create objects that represent your rooms and shelves- either to scale or in an arbitrary size, then you can link up these entities with your existing databases to show catalogs, movement and more. A similar innovative use is to use a GIS for mapping hospital beds for availability and management- this gets very useful for tracking the outbreak of common hospital infections or for serious outbreaks that can occurr in a hospital setting.