Is FBX capable of exporting Houdini attributes into the format; attributes as in what you would promote for the asset ?

I don't think so, you probably want to use Alembic .abc files instead. Or use .bgeo.sc files. They can hold attributes. It depends upon what target application needs to read the resulting file.

I see the limitation; I suppose Houdini Engine is the best solution for Houdini Digital Assets. Alembic needs to pack Houdini Assets into it's file format.