When the phone is turned on, the phone communicates with cell towers. This can approximate your location. To be truly anonymous (as much as possible) you should have the phone cut ALL communication with the cell towers. When you make the call, the antenna turns on, call is made, antenna turns off.
Additionally if the phone can be configured to use wifi for phone calls, then ideally you decrease the possibility of the location being tracked.
If the phone is on in theory authorities should be able to pull records from the cell companies and track every place the carrier of the phone visited.
For added shipping security always ship from a VERY high volume shipping place. This way its hard to isolate your package, but not impossible.
I think the ideal way would be to make the device a passive satellite receiver. Then when a phone call arrives for your device, the satellite broadcasts a message which your device can passively receive which tells it to wake up and get on the cell network.
In theory you can do this with cell towers (it's how pagers work -- you may even be able to reuse the existing infrastructure), but in that case you either have to know somehow which tower is in range of the device (which obviously leaks the device's general location) or you have to broadcast on all towers everywhere (which, as wireless bandwidth increases, becomes increasingly practical since the incoming call message would have nearly trivial length).
Since pretty much every place I tried to use one on the Internet does address verification when processing the transaction, they simply don't work.
IP address
> call the number
Phone number
Careful.
edit: I see in another comment that you're adding this (https://news.ycombinator.com/item?id=5840440)
Also, if you want to prevent tracking at the USPS -- ship the phones in unmarked boxes with postage purchased with cash. Don't use a return address and randomize the post-offices drops you utilize to send the packages.