I'm not really up on my phone'ism's to know what exactly you mean by turning off the radio.
However, GPS on phones and especially GPS on AT&T iphones, I do know about and maybe this will transfer to your application.
Both of these eliminate signal searching and extend battery life.
Settings>Airplane Mode to ON, GPS is disabled as well as the rest of the data/cell signal.
General> Cellular, set of OFF stops the searching for cellular signal and data.
GPS in a cell phone is a separate animal from the cellular / data, in that GPS does not need a cell signal to function on a cell phone. Shut of Cellular and GPS will still function.
HOWEVER - the map must be previously downloaded to your phone in order for the GPS to show roads, routes, etc... If you do not have the map/route downloaded all you will see on your screen is an arrow pointing and no roads.
Just this weekend on the way through portions of AL, GA, NC and TN, no cell service in a lot of areas, but no problem with the downloaded maps.
Running MotionX GPS and MotionX Drive on my phone, MotionX GPS I've used in 4 countries with good results.
For power I'm using the stock power outlet and added an always ON outlet, with the normal phone cigarette charger from some convenience store, 30K miles and some heavy downpours no issues.
Good luck with your trip, little GPS prep work and it's no sweat.