james_s: Sure. Apart from looking cute (and yes, we all remember screensavers were once a whole new market!
), I can see one benefit: the user has a visual hint that the system is running. If the screen is off, it may not be so obvious.
If that's the point here for the OP, I'd suggest the following (which is what many mobile phones with OLED displays do for notifications): to show the system is "on" while the display is off, just use the display as you would use a LED (OLED displays are perfect for that): just flash a line of pixel every second, or something like this. It won't be as bad for lifespan as animating fancy stuff, and will draw minimal power on average as well. Maybe that's what the OP had in mind with their screensaver. But the point would just be briefly flashing simple shapes on screen. Even if it's always at the same spots (like a thin frame all around the display), if it's only briefly flashing, it'll be fine.