No, the official Xbox 360 Wireless Headset with Charge Cable (often called "Charge & Play") has no power button.
To force it off immediately: Unplug the USB cable from the console (if charging) or turn off the console. There is no user-accessible switch.
LED Indicators: Green = Charged/Connected; Red = Charging; Blinking Green = Pairing; Blinking Red = Low Battery.