Yes, you do have some control over the special "Off" activity button, but indirectly via the device power settings feature, which has 3 options:
1) I want to leave this device on all the time
With this option, the activities (including the special "Off" activity button) will no longer control the power of that device. However, the activity "Help" feature will still track what the power state should be, and will issue the appropriate power command when invoked.

2) I want to turn off this device when it's not in use
This is the standard option where the activities (including the "Off" activity button) control the power of that device.

3) There are no power buttons...
With this option, you will have to control the power manually or via the device mode.