The file geodatabase API/SDK should support any coordinate system ArcGIS itself understands and can use.
After days of troubleshooting why our file geodatabases could not be read by 3rd party tools utilizing the FileGDB API
I discovered and verified it's because our local coordinate system is not in "the list" (http://trac.osgeo.org/gdal/ticket/4578). This is really a surprise and an unexpected limitation coming from the company that in many circles is synonynous with the word GIS . Please fix.