Harold Kestenholz
The earth connection is a nicety that routes transient electricity around the water in the hose. Theoretically, as water has resistance, the water in the hose could boil from large quantities of electricity, so electricity is routed around the hose through a better connection.
All the internal electrical devices should work without this earth wire. However, it is a good idea to add an earth wire from the sheetmetal of the washer to the metal grounded plumbing to honor the intent of the manufacturer. A build-up of static electricity would also be prevented.
