You can't place overlays over props. They can only be rendered on world geometry.
For this request, you're better off making several brushes shaped like the wooden sign prop itself with a little bit of vertex editing and the clipping tool, and then turning each brush into func_detail individually. Afterwards, you can use the overlay tool to place whichever sign on it (but you'll need to go into the overlay's properties and select multiple brush surfaces so that it may render properly on all brushes).