Hello Phantogenic,
I already did that to see what happens, even if I don't want to have my S3 visible from any other unit, but it is always the same: deactivated within the next 2 minutes.
I don't use any battery saver (I tried two years ago, but I found these softwares totally inefficient). To cut off BT, WiFi and decrease the screen brightness, I can do that manually very easily.
The WiFi stays on without any trouble.
BR.
Daniel.
I forgot to say: I don't use the "Energy economy" option neither.