Japan: Can I ground a dishwasher by connecting it to a sink?
You can't rely on the integrity of the ground/earth on the pipework of the sink. For all you know it could be connected to PVC pipework further down. In the U.K all pipework is meant to be cross-bonded which is then taken to the earthing bar. However in Japan I am unsure if this is what is done. Regardless you should be earthing/grounding it back to the incoming supply. 

In a lot of countries that use two pronged devices they are actually fed from centre-tapped transformers or are double insulated devices. Either way they should not become dangerously live. 

In short don't connect to the sink run it back to the earthing/grounding bar.