It depends quite a bit on how the screen is updated. If it's like a traditional raster image, then you have to clock out each individual pixel in the image along with some blanking periods. The controller on the display is then responsible for taking that pixel data, syncing on the blanking periods, and drawing lines of pixels whenever data enable goes high.
If the eInk display doesn't use this raster model but rather an addressing model then it might be possible to support partial updates. I doubt very much that it does though.
Eink uses a raster mode, but with (somewhat) tri-state pixels. You can send a 'no change' to any particular pixel. The disadvantage is you still need to scan the entire screen, so it isn't really useful for changing individual pixels, but partial updates are common.
The other difference from a traditional raster display is there is no minimum refresh rate.
Eink controller chips use an addressing model and handle the partial updates for you, so the main processor sees a bare framebuffer.
Note the link I submitted above, where it says that yes you have to send all rows with every refresh, but for every row you can tell it not to do anything. Presumably that means if you skip all but few rows, you'll get a faster update.
If the eInk display doesn't use this raster model but rather an addressing model then it might be possible to support partial updates. I doubt very much that it does though.