Yes, but is it genuinly turned off? It is possible that there is some power used in the circuits that detect when the power button is pressed to start the reader again. But most likely that power consumption is much less than the selfdischarge from the battery, so not really noticeable.
The fact that the same button is used for both types of shutdown (full/sleep) suggests to me that the button is more than a simple power switch that completely breaks all power consumption.
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