ArcGIS does not support AutoCAD Object data tables. The Export capability of ArcGIS Map 3D or Civil 3D to shapefile also does not consider the .WLD file. At that point it is just a GIS shapefile all on its own.
To georeference a Shapefile you really just need to move/spatially adjust it into place. ArcGIS for AutoCAD is designed so that you can create attributed feature class data inside AutoCAD that is georeferenced so that you don't need to export to shapefile or georeference your data. ArcGIS desktop will read the attributed featureclass data soley in the DWG and you have tools in ArcGIS for AutoCAD to draw in an explicit real world coordinates that you choose.
If you haven't seen them I have created some videos that might help explain different ways to create and edit ArcGIS data using ArcGIS for AutoCAD.
ArcGIS for AutoCAD Training Series:
https://www.youtube.com/watch?v=1IADtVQi6h4&list=PLHTg8zWG0OuktrJAz1rQTEad9-HNAziqr
-Don