The issue with this idea is that the NetworkManager service takes its commands from nm-applet (or the KDE analogue, if you're in KDE. To avoid confusing myself, I'll assume you're in GNOME). There is a command-line NetworkManager interface in the repositories called cNetworkManager (that's, oddly enough, written in Python). You could try to stick a command to connect to your network using cNetworkManager in a startup script (I'm not entirely sure where you'd have to put this script, but I know it's possible :D). I don't know whether or not this approach will connect or if it'll stay connected after you logout, but i DO know that there are at least 2 issues you'll have to reconcile.
1) You'll have this script fighting with nm-applet. If you want to do this, i'd disable nm-applet from starting automatically (which should be configurable in either preferences -> sessions or preferences -> startup programs, depending on whether or not you're using fedora 11).
2) if you ever want to change networks (and do fancy things like automatically detect them), you'll either have to do so using cNetworkManager (which is a real pain), or start up nm-applet and lose your ability to keep the connection open after you logout.
Best of luck, and let us know if this works!
Also, it's not working for me on an odroid running the provided Ubuntu 14.04 image. – Andrew Wagner – 2015-08-18T14:02:51.900
This answer (and linked documentation) is obsolete, at least as of Ubuntu 14.04. The obsolete info in that FAQ, of course, has not been removed. – Andrew Wagner – 2015-08-18T14:48:54.163
As of May 2011 that link says: On version 0.7.1 or later edit the profile of the connection you with to start prior to login and select the box in the bottom left "Available to all users" – Joe – 2011-05-04T13:24:46.563