There is no way to export out georeferenced maps from layout view.
To quote the ESRI help:
"To add georeferencing information, check Write World File. This option is only available when you export while in data view and creates a world file that contains information that is used in conjunction with the exported raster file to tell software where the image is located in the world. The file will have the same name as the image file and a file extension that is based on the first and last letters of the image's file extension plus the letter w. (For example, if you create a TIFF image named MyMap.tif, the world file is called MyMap.tfw.)"