No...Software Update only connects directly to Apple's servers, so third-party apps can't use it. Apple is obviously very protective about its protected systems for deploying trusted updates. Allowing other companies to have access to that system (even if each update had to be approved by Apple) opens the door to significant security breaches.
While it would be nice to expand things, it's understandable why it's limited to Apple apps.
The three apps you mentioned: adium, skype and firefox all have the ability to check for updates automatically. In adium, select check for updates, then check the little box where it asks if you want to check automatically. In skype its on the general preferences pane. I think firefox does it automatically whether you want it to or not (since I can't find where you would turn it on/off). Hope that helps a little.
I wish this was an option on all software, though I can see reasons why a small developer wouldn't add it right away as a feature.
Actually its normally the smaller developers that include Sparkle (the update systems in Adium etc)
It takes a few clicks to set it into your program
Dragging this up a bit, but I found an app that does exactly this
Anyone tried using this? Sounds interesting!
Yes, not only does it work, but its worth downloading just for the beautiful UI...really well made
So the fact that it uses a French server doesn't seem to cause you any problems, does it?
No...I am in the UK, but have no idea how it would affect US users...