I have noticed with Firefox 3 if I ignore its updates for too long it goes to 100% CPU and stays there until I kill it in Task Manager, then on restart it installs its updates. This never happens unless there's an unapplied update waiting...
The way I configured it, it checks for updates to addons every few hours, and if it finds one, installs it silently. The next time Firefox starts, it's ready to go - basically, it does the same thing as a manual check, install updates, but instead of clicking the "Restart Firefox" button, just leaves me alone.
I hope that's basically how they do it... it really would be background - except for those that don't restart Firefox every week or so... but at least for me, addon memory leaks still cause me to restart Firefox every other day or so (I have -- oh, this is great! I just counted - I have 42 extensions installed. hehe)
Your browser session is never interrupted, and in fact no update alerts are ever shown. Just once in a while when you start Firefox it's the new version that it installed sometime during your last session.
It makes me think it will be like the current behavior without the dialog asking to install (e.g. automatically download the update and install it when you restart your browser).