Some (all?) of the builtin programs auto connects when needed (at least the browser and app manager does so IIRC). However I can't think of any 3rd party apps auto connecting - fennec and faster app manager certainly doesn't.

For a "mobile computer" the internet connection handling sure sucks. And Nokia sure sucks always taking 1 step forward and 2 steps back:

The E70 had a connection groups feature, each connection group consists of 2 or more internet connections which will be tried in order of preference. Then in each program you could specify whether to ask which connection to use each time or you could specify auto use a connection group or an individual connection. This worked, mostly. But with the E71 this concept of connection groups was removed !!!???!!!