Copper and gold plating of pcbs right around board edges is possible. Not  (normally) 100% as tabs are required to hold pcb panels during processing in chemical baths, to accomplish copper deposition etc.. The technology  is called castellation and is normally confined to parts of holes as per 3D image on left below. By using castellated holes it becomes easy to make components for other pcbs, with pcbs.  We have supplied very small pcbs,  sometimes punched such pcbs smaller than  5×5 mm in 0.4 mm thick FR4 material, for example.

 

 

Explanatory 3D image of castellated holes        planar pcb transformer with visible top coil and ferrite