Your monitor pulls power from the wall.
Your computer also pulls power from the wall.
The only thing being sent to the monitor by your computer is an unpowered digital video signal.
The graphics card will only use less power if it is taxed so little with the lower resolution that it decides to downclock itself, which will rarely happen if you are really playing a game.
Your power consumption should be worried about if you have a limit on what you can afford or are able to draw from the wall or if you have a terrible power supply. In the case of a low-end power supplyl (say 350w) then you should use one of the many on-line calculators to estimate your system's needed wattage, and buy a new PSU if necessary.