Based on a single line in a Washington Post article, Privacy International has been investigating whether it is possible to track cell phones when they have been turned off. Three of the 8 companies they contacted have responded.
In general they said that when the phone is powered down that there is no radio activity, BUT that might not be the case if the phone had been infected with malware.
It is important to remember that the power button is not really a power switch at all. It is a logical button that tells the phone software that you want to turn the phone off. The phone can then clean up a few loose ends and power down… or not. It could also just behave as though it were shutting down.
They don’t cite any examples of this either in the lab or in the wild, but it certainly seems plausible.
If you really need privacy, you have two options (after turning the phone “off”):
1) If you can remove the phone’s battery, then doing so should ensure that the phone is not communicating.
2) If you can’t remove the battery (hello iPhone) then you need to put the phone in a faraday cage. You can use a few tightly wrapped layers of aluminum foil, or buy a pouch like this one.