Will my productivity really increase?
For the first few days/weeks, absolutely not.
After you stop having to read through the tutorial every time you want to edit something - sure..
Emacs is more "powerful" than vim, it's scripting engine is far more flexible, and there are far more scripts, modes and the likes built around emacs.
That said, the opposite is true.. If you spent the same amount of time improving your knowledge of vim, you'd could be just as productive..
Maybe not productive in the same way - I'd say vim is quicker for editing files, emacs is better at doing everything else (again, I would personally say things like flymake-mode, VCS bindings are such are quicker to use than the vim equivalent)