It depends on where it's stored. If you use up all your RAM the GIF is stored on disk if it is scrolled off the window. GIFs stored on disk do not move.
If you have RAM available it is stored in RAM. If you scroll down and the GIF is stored in RAM the GIF is still processed through the processor meaning that it is still active. In this case when you scroll to view the GIF again it is taken from RAM and sent through graphics to the monitor.
Some would say that if a GIF is not displayed it cannot be moving since movement would imply something that is displayed on the monitor. Others would say that if a GIF is stored in RAM it is still moving in RAM by virtue of the fact that RAM is causing it to move even if it isn't being displayed.
