No, the layer "structure" does transfer , IF you select the option "Original" under Component properties. But not the categories. ( RMB the component in the ANT- Properties)
The other option in that dialog will place everything from that model on a single layer in the drawing file.
The categories is only a "nickname" which you give to a couple of layers, such as "Sketches = Layer 21-31"
The "normal" procedure is that you set the categories in your template parts, then the same category names will exist in all your files. ( if you decide to set it like that. )
We have a special category in our drawing parts for "things" we would like to hide on the drawing, so instead of waiting for a couple of thousand fasteners to be hidden line processed, we move these fasteners to this special layer category in the drawing file .( this category is set invisible)
If you have many templates in which you want to create the same categories, this operation can be automated using a Journal .
If you intend to use the same catagories in all models and drawings in the future, I would include them in your seed and template parts.
Please consider using the existing example utilities provided in
which can be run from "Tools, Play Journal" (ribbon user interface).
Hope this helps,