Hi Grant,
as Lex mentioned, Project Organizer doesn't show symbols of all files - that would be way too many symbols to display for big projects. The Project tab in the sidebar shows all the files belonging to the project - that is, those files that match the "file patterns" and are inside the "base path" that you specify in project properties. When you enable indexing of the whole project, Ctrl+clicking a symbol (e.g. a function name) works project-wide and takes you to the function declaration even when the file isn't open. You can also use Project->Find Project Symbol and here you can enter the name of the symbol you are looking for (you can set custom keybinding to this menu entry if you need this frequently).
Cheers,
Jiri