Hello,
If all you need to do is georeference your dwg files I suggest using the Data Interoperability SpatialETL tool. Set up the SpatialETL tool to read and write DWG (the dialogue boxes will lead you through this). Once the SpatialETL tool is created, go into the properties of the destination DWG dataset in the Navigator pane on the left and set 2 parameters: the "Coordinate System" and "Coordinate System Storage" (I've attached a screenshot of what this looks like). For "Coordinate System Storage" you can choose from "External PRJ", "Internal ESRI WKT" or both.
The Data Iteroperability Quick Import/Export tools will not give you access to the "Coordinate System Storage" parameter I just described.
I'm not sure about the ArcGIS Direct Read + export features.
Hope this helps,
Mita Hajirakar
Safe Software Inc.