Yes. BUT only if you tap it, and do NOT hold it. The usual method is to navigate to the browser menu and select 'Power Off Device'. In either case, a dialogue box will open and ask you to confirm. If you tap the power button again or click 'OK', the console will power down. Either method is completely acceptable and accomplishes the same task.
However, some consoles running Windows7 do not have this feature. If you press the button and nothing happens, please use the browser menu to shutdown.
Unless your console is already locked up and you have no choice, pressing and HOLDING the power button to power down your console is NOT recommended, as it can corrupt data on the hard drive, lead to corrupt shows, cause odd/slow behavior, and cause the console to lock up. The same goes for the power switch on the back of the console. If you are having these issues and suspect this has happened, you can find out in the logs, and a reimage may fix the problem.