Yes, if you press the power button the display turns into standby. It is still on, though (and the RAM drains battery). On my S200, keeping the power button pressed will allow you to switch it off completely (a cold boot is then necessary like after a soft reset).
To change the SIM you need to remove the battery, but my friend is afraid to do so unless the device is switched off completely. According to the manual, however, you cannot do this. So I was wondering if it's risky to remove the battery while the device is in standby.