I faced a similar situation recently, and it turns out that ESRI has not
released the API for exporting rasters from a geodatabase. Interestingly,
they have released the API for vector files. Here is some additional info:
If you have access to ArcGIS and ArcPy, there are Python scripts to export
rasters out of geodatabases that can then be imported into R using the
raster package, etc. Otherwise, you may be out of luck unless ESRI has a
change of heart.