I can import CAD files (using CAD to geodatabase) but when I try to georeference the layer it isn't being recognised as a CAD layer, meaning I can't use the georeference tool.
Were the CAD imported with any pre-existing projection/georeference? I've had engineers send me CAD files that were georeferenced in their software but the georeference didn't translate properly to Arc. In those cases, all I had to do was Define Projection and it snapped to place without the need for CAD georeferencing. If that's not the case, which I assume it isn't, have you explored using the Move tool in the editing menu? That can get laborious quickly, I know, but might be a quick way out of your problem.