You don't need scientific research to know that a good extensible, programmable editor that can become an extension of your mind and hands is going to make you more productive than Notepad. It's like playing a musical instrument. The finger movements and thought processes move into the background over time as you master them with proper practice and you start operating at a higher level. A world-class musician isn't thinking about which notes to play when and where to put their fingers but rather how to put more emotion into a performance.
Similarly, a top flight programmer who has mastered emacs or vim or Sublime Text won't be operating at a conscious level but will be controlling the environment in front of them at a far higher level, especially if the conceptual model of the text buffer is the same no matter what they're doing with it.
An extreme comparison would be to sit two people of the same ability down in front of the Linux kernel source tree, one armed with emacs, cscope, syntax highlighting, org-mode and cc-mode and the other with nano and see who is faster at some non-trivial task.