EDIT: If you use the FileBrowser dock to move files, the editor will attempt to update most references (Godot 2.1.4). I did this recently on a game and it worked, I just had to close open files in the script editor and change some scripts because they were referencing old paths.
I don't think there is. This is how Godot works. In theory it can be implemented, by fetching every file in the project, searching for places where the path is written and replace it. But it would only work if all format is text, if there are binary assets (.scn, .res, .msh...) they will have to be loaded first and checked for every reference, making the process more tricky. And even more, some assets may reference the asset with a full path, others with a relative path (including scripts!).
So... it's not built-in, it's doable, but not trivial. For now you have to use the dependency fix dialog, or write a plugin.
Edit: also, there might be a way to actually improve from the dependency fix dialog, which actually fectched the places for us.