No to both of your questions, bobgoe.
The screen only consumes power when it changes (e.g. turning pages in a book), the static display of an image doesn't need any power.
And there won't be any burning effects. What you most probably will experience is an effect that is called "ghosting". After turning on your reader again it may be that you still see some "rests" of your boot off logo. But this disappears after a screen refresh.
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