I attempted to splice my ammeter directly between my D50's battery and the camera with some electrical tape and aluminum foil (seriously). It worked, but the ammeter dropped ~0.6v out of 7.4v that the battery puts out, and that was enough to keep the camera from being able to take pictures, but it could operate in standby.
In any case, the camera itself draws about as much current as the EyeFi card does. I think the real power sucking this. The camera (either off or in "standby") with the "Meter-Off" takes a very small amount of power. Powered on, it takes probably 40 or 50 times more. Following those EyeFi directions means that you put your camera into this higher power consumption mode for 30 minutes if you take one picture instead of 16 seconds like it might have before.
So, my guess is that the power consumption comes more from the camera itself than from the EyeFi card. But, the only reason to put your camera in that mode is for the card in the first place. Anyway, I bet this is exactly why EyeFi and Nikon are working together on the D60 and EyeFi card integration.