I have just purchased the latest gen kindle paper-white (2016 300ppi) and received a case with a magnetic cover. Doing a little testing with the magnet in the corner, I can see that even when I turn my kindle screen off using the button, the magnet being pulled away powers it on. When I place the magnet on the kindle again, the kindle displays the screen-saver rather than turning the screen off.
From what I understand about e-ink technology the technology is bi-stable meaning the actual display of the image doesn't drain power, its the refresh of the page (as well as wifi, the back-light, touch response and the cpu processes). On the lowest brightness setting the kindle has an almost unnoticeable light source which can be seen in the dark as a glow. When I use the magnet and the screen-saver comes on, the light appears to shut off completely.
That said, a number of sources on-line say this light stays on when the screen-saver is displayed which will still drain the battery over a long period of time. I don't think this to be true but I can't confirm it either. Is this true of the current gen model, older models or not?