Room temperature water would be entering rather than cold ground water

Um... could you rephrase your question in full? I'm having a hard time understanding what you're asking exactly? :confused:

The water heater will require less energy, but the room will be slightly cooled (as a result of the cold water sitting in the holding tank cooling the room off). If you're also using energy to heat the room (from another source), you may not be saving any energy overall. On the other hand, if this room is naturally (i.e. without any man-made heat source) warmer than the temperature of the ground water, then yes, you will save energy this way.