We have a "secure" checklist which should be used for when a crew are not handing over the aircraft to another crew. Turning off the ADIRS is not on any part of our checklist but if handing to another crew they have to do a full align so I tend to switch the ADIRS off if I will be leaving the aircraft. If its another sector for the same crew we do a quick align unless they have drifted off alot during the sector and then we'll do a full align.
Our secure checks include those items atomic mentioned, although if handing over to an engineer we generally leave the APU running.
It is my pet hate when crews decide to do a secure check and turn all the screens off, all the radios off, and all the lights off, when I am waiting at the door. So if you do that. DON'T!