Does it?

Not it does not. Since it is gas all you need are inlet/outlet lines and a gas connection to make it work. The only other time you might need to plug one in is for a electric pilot light. It would provide the spark for your heater to ignite. Older models used a tube and low pressure to keep a flame burning for ignition.

Direct vent gas water heaters also require a 120 V connection.

There were times and places where the grounding of the home electrical system was done by clamping the ground wire to the water line and most of the time it was to the cold water line at the water heater.

Actually, you would be wise to bond the cold water intake line to the hot water out line. This way all pipes are at the same reference point.

Need a more specific outline of your question. Are you talking about grounding, or actuall voltage supplying a water heater. Standard water heater requires no power supply. Side vent or direct vent water heaters require 120v supply to run draft inducer and ignition module. As far as grounding between pipes on hot and cold, yes, it used to be done, but it all depends on what type of piping you have these days. Many homes are piped with pex(plastic) pipes, so grounding to the water piping is not an option.