I think you're quite confused. Emacs always avoided a huge startup hit by loading elisp code into temacs (bare bones emacs that only exists when building it) and then dumping it with unexec to produce the emacs that is distributed. A decade ago, glibc stopped supporting unexec and emacs had to switch to a different method of incorporating the elisp code and avoiding the startup time, but the unexec code was still there. Now, a decade later, that code--which was not being used--has finally been removed.
None of that has anything to with emacs vs vi -- the point that your professor was making was that vi was distributed by default with UNIX so it was always there, whereas emacs needed to be installed (which wasn't even an option on servers).
Well, this was over 30 years ago that I was sitting in that class, and the resources the emacs required vs vi was definitely part of the discussion. We were working in a shared environment on a solaris system, and if the whole class fired up emacs for a class session, the effects were definitely experienced by all the users on the system at the time.
I'll add a little context. I mentioned that it was 30 years ago. My personal computer at the time was a 486DX-50 with 16 MB of RAM, and the mainframe we were tied to had maybe 2 GB of Ram? For 200+ users to share. It's easy to forget how far hardware has developed since then.
None of that has anything to with emacs vs vi -- the point that your professor was making was that vi was distributed by default with UNIX so it was always there, whereas emacs needed to be installed (which wasn't even an option on servers).