I regularly have co-workers generate CAD drawings with a coordinate system in AutoCAD/Civil 3D, the entire drawing can be brought directly into the correct location in ArcGIS as long as the coordinate system in ArcGIS is the same as the one used in AutoCad. The data still will not have a projection however, it will however be based on the same coordinate system and come into the proper locaiton. I usually convert the CAD drawings to a shapefile or GDB by the type (Annotation, Point, Polyline, Polygon, Multipatch) and then define projection for the output files.
You will need to check with whomever created the CAD Drawing to see if it had a coordinate system and if so what is was.