That's a sensitive matter in Japan you know. So yes they should worry about it and I think it's a great idea if it can be configured by the player.
Bonus: Add an auto GPU limitation feature that would cap the frame rate at 5~7fps while being AFK for an extended period of time. I personally lower my framerate cap at 30fps when I don't need to do anything gameplay related. It saves power, especially with power hungry GPU (hi2u GTX580).
If you just want to leave your character online overnight, framerate doesn't matter.