Being new to Emacs, I am wondering if you could enunciate how these gains might come in a particular case -- of course, a hypothetical one. Suppose Joe User has configured Auctex on a squeaky-clean Emacs 23 installation. Joe had been trying to understand coherent sheaves and Serre duality, and so, having spent the morning reading "Lectures on Riemann Surfaces" by R.C. Gunning, he took some notes with paper and pencil. Then, he wrote a corresponding set of notes in his brand new Auctex system. It was all running and well, and Joe C-x C-s'd and went to bed and dreamt of Gammas and Pics and Strange Os. Joe woke up the next morning and went into zazen, looking at the sun rising through the treetops in the forest behind his home.
And he did it again that day, and made a bit more progress, and learned a beautiful proof for Weierstrass's theorem using the induced sheaf cohomology of the exponential sheaf sequence. Joe decided to use Windows XP -- he didn't want to think about all that lisp stuff today, and having nothing but Internet Explorer 6 (Joe only reads one page at a time) and Notepad to do his work with, he wrote the rest of his Latex notes in Notepad. And he felt happy, and went to bed -- which wasn't a bed, just a floor, as Joe was really a minimalist sort of guy.
How will Emacs enhance his experience (in any broad sense)? He doesn't compile often. Come to think of it, he probably doesn't need the preview-latex function either. In which forms do these gains come for him? Generally, what is the least complex form of editing that Emacs can still produce gains for?
First biggest productivity gain for Joe will be in using forward and reverse search for navigation (C-s and C-r in default key bindings).
C-s or C-r, type a few chars, <Enter>, continue editing
is an amazingly powerful way to jump around even a simple text file. No arrow keys, no mouse. I dare Joe to use this feature for a few days and try to go back to Notepad. (You'll be using it even to jump to a different point in the same line.) Also Emacs can be as minimal as you want it to be.
Any data formatting and parsing is extremely simple and easy, since this essentially becomes programming by doing. Much quicker than any other method I know and awesome for the many, many quick hacks one needs throughout the day.