Yes, if the [Auto Power Off] feature is enabled in the Device settings, the printer will turn itself off automatically after the selected period of inactivity.
Available settings: [Off], 10/30 minutes, 1/3/6/9/12 hours
<Adjusting the Auto Power Off setting>
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Connect the printer to be configured to the computer.
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Start the Printer Setting Tool.
To learn how to start the Printer Setting Tool, see "Using the Printer Setting Tool (for Windows)".
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The [Printer Setting Tool] screen is displayed.
Select the printer and click the [Device settings...] button.
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The main window is displayed.
In the Basic tab, select the desired settings from the drop-down menus.
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Click [Apply] to save the settings to the printer.