I can see the value in this, especially when a PDM system is being used. For example, if you are pulling the drawing number and description fields into the title block from the referenced part/assembly and you do not also have these custom properties in the drawing file, you will not have these properties available when looking at previews of the drawing or when searching through the PDM system. You will also not see the description show up when you highlight the drawing file in Windows Explorer, nor will you get the description in the windows status bar (both very useful). In my opinion, it is best to have the description field in both places - part and drawing, which is what is being requested.
The best way to do this is to use a VBA form to enter/modify custom properties instead of using the SWX interface. This is very thoroughly discussed in the API help and there are numerous free custom properties routines available. You will need to modify one of these to accomplish what you are after. Then, you can enter properties as normal in part and assembly files, but when a drawing file is active your routine needs to:
1) get the first drawing view
2) activate the referenced document
3) get the properties you want to transfer and store them in strings
4) return to the drawing document and update/create the corresponding custom properties in the drawing
In this way, model custom properties can drive drawing custom properties without manual retyping. A macro will do it and is a better solution than a macro feature.