I'm sure you know the relevant setting is Tools->Settings->Connection->Packed Data->Packet Data Connection. You only get 2 options 'When Needed' or 'When available'. Neither of these options is particularly useful or descriptive, but we are stuck with them.
I use 'When needed' which is the default. What this does in practice is force most apps to ask you each time they want to connect to the internet and this allows you to have the option of blocking connection if it's going to cost you roaming charges. You need to check each app is setup properly for this to happen (all the installed ones are) but some apps need to be configured so that they ask.
If you use 'When available', you won't get any notification that an app is connecting, and my concern (not proven) is that the danger is roaming charges may apply if you wander out of a coverage area (such as go into a shopping centre) or if you exceed your download limits.
Either way, it seems, the phone will be 'connected' to planet 3, whether any internet apps are open or not. Even if you manually disconnect the planet 3 connection (and it's quite easy to do) the phone will reconnect by itself. But if you have the settings I suggest above, you won't actually have any traffic charges because you won't be using any data. It's just an open connection for reasons that make no sense to me. But as far as I can tell there isn't anything that can be done about it. (MyE63: There is a way to stop planet 3 from automatically maintaining a connection.. see the previous post for now for a brief explanation how).
At first I was quite alarmed, but I've had my first bill now and don't have any surprise usage charges. Whether this is actually using battery power I don't know.
Finally (yeah, long comment, sorry) one general tip for all phones is that the more (reception) bars you have, the longer your battery life. Less bars mean the phone is struggling for a connection and will use more energy searching for a better signal or to boost the signal it's got. If you get more bars by leaving the phone on a window sill rather than in your pocket, you can save battery life that way.
Thanks for your suggestions Matthew!