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Shouldn't do.
Eink doesn't use power all the time an image is displaying - only to get the 'ink' particles into shape in the first place.
You could argue that using a standby screen picture would count as a page turn to bring up the 'screen saver' image, adding very slightly to the everyday battery use. However, the screen will flash black before clearing itself to a blank screen anyway, which is equivalent to a page turn. If you leave it without being in standby, the touchscreen will probably remain using some power.
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