All of the attributes of all the fields of every feature layer are automatically included when you use EXPORT TO CAD. To see the attributes and feature classes in AutoCAD just use use the free ArcGIS for AutoCAD plug-in from Esri. If you want to have the block attributes included for display purposes you can also include the name of a block in the REFNAME field of the output POINT feature layer. Using a seed file that contains that block name and that has ATTRIBUTES with TAGNAMES that match the field names you can populate the blocks with the field values where those names match. You also need to make sure that you include the field ENTTYPE and populate the values with INSERT to override the creation of simple points with INSERT entities. So you need REFNAME with the and ENTTYPE with "INSERT" and then field names that match TAGNAMES, AND you need a seed file with those blocks defined.
Know that you don't need any of that if you just want to use the attributed feature classes that are already there in the AutoCAD drawing by default! To see what you've been missing download and use the free ArcGIS for AutoCAD application from ESRI. POINT, POLYLINE, ANNOTATION and POLYGON feature classes are all fully attributed by default and without a seed file or messing around with the output fields. The best form of interoperability for exchanging files between AutoCAD and ArcGIS is just EXPORT TO CAD and the free ArcGIS for AutoCAD plug-in. You can see this everytime you EXPORT TO CAD, since if you look at the .DWG file you create with ArcMAP or ArcCatalog you see the .DWG file with all of those feature classes inside the drawing when you open up the blue folder. ArcGIS for AutoCAD sees those same feature classes.
ArcGIS for AutoCAD is free and also allows you to create ArcGIS feature classes in the drawing and access Map Services, Image Services, and edit Geodatabases through ArcGIS Server feature services.