Recovering lost or stolen phone (security and feasability considerations)?

I am trying to understand a little bit about security in case my phone goes stolen. I have read that even if a phone is stolen and the SIM card is removed, it can still be possible to find your phone because the hardware has a built-in International Mobile Station Equipment Identity (IMEI) number which gets transmitted at regular intervals over the mobile network. Apparently this number can be changed in the software in the same way that, for example, the MAC (Medium Access Control) number of a hardware device such as an ethernet card can be faked on Linux via software methods, but it appears that doing so is not legal in most countries as it could help people stealing your device. So, here come my questions:

• Am I correct in assuming that if the device is turned off (either manually, or perhaps because the battery runs out), then presumably the IMEI cannot be tracked until the device is turned on, which means that the device can go lost this way? Or is there some Android app which can reveal the location of your phone even when the phone is powered off (perhaps a phone which is powered off still uses a minimal amount of battery to make this IMEI information available to the carrier, or maybe via GPS given that GPS does not require a SIM card to be present to operate)?

Thanks.