A lav with overflow protection has a space below that junctions with the overflow from the top of the bowl. The drain has holes that allow the flow to drop downward and into the lower portion of the drain.
If as part of manufacturing that use a plug, and that plug is leaking, I would find a way to seal it.
Removing an undermount is not fun. It won't be under pressure, so I wouldn't think it would take much to seal it.