]I'd like Adium to be invisible (except for the menu extra), and appear only when I'm receiving a message.
I'm not quite sure what you mean by invisible. iChat, like Adium, is an application and the only visible elements when not chatting is the buddy list, which can be closed, and it's Dock icon (plus the menubar extra if you choose).
If you just want to get rid of Adium's contact list then go into Adium, click the Window menu and select Contact List to show or hide it.
The only thing you'll see then is the Dock icon or you can elect to have it notify you in various ways.
I don't know if Adium has a menubar extra...