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Actually, even when powered off it'll show the cover (though this can be turned off in the Power & Sleep settings). This is normal.
As for the power issue, showing the cover does not affect power use at all, beyond the power used for the initial drawing. For eInk screens, power is only used when drawing the page, so it's not consuming power when in sleep mode. In sleep mode, what's drawing power is stuff other than the screen, such as the wi-fi antenna (if wi-fi is on) and RAM (which needs to be powered so that the book/home screen opens instantly when you come out of sleep, rather than having to be loaded from the internal storage card).
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