Is it possible to use Automator to script an arbitrary scriptable application the way it is possible to load the application's dictionary to Script Editor and use AppleScript to script it?
If I understood what you want...
What you got on the left side of Automator (Action Library) is basically that.
Here you can see an example of Transmit Automator Action showing up in the menu.
If you can't find application Actions there, then it's likely that the application doesn't support Automator. In my personal experience, not many applications do.
Although sometimes they fail to show up in automator. If that happens, I'd check the application contents (right click > show contents) and find a folder that contains the automator actions. You can then just open the files and Automator should open up and ask if you want to install the actions. It should move the actions to
Automator is often used to create a trigger for scripts, since it's more common for applications to have Applescript support. Alternatively you can just force things to happen in the application by navigating the application menu with a script or triggering shortcut keys the application supports. Of course you can also use countless other applications for triggering scripts, it doesn't have to be Automator.