You can put the icon for any app on the Dock. Just go to your Applications folder and drag an icon to your Dock. Or, if you have the app running, just right-click on the Dock icon and select:
Applications do not live in the dock; only links to the applications. Applications run from the applications folder. I don't even know if the dock is even a real directory anyway.
The closest thing to what you mean, would be this: see picture below
As the Dock is not a directory, as was slightly said above. The Dock can only have application-sensitive menus, AFAIK. However, there are menubar applications which do the thing you seem to want, look at Menuet and ByteController