On reading this thread on the NMM forums, modified files are not replaced, rather they are overwritten. By this, it means that each time your game loads, it checks your load order, and overwrites files one by one as your game loads. For instance, when you use a texture mod, the game calculates overwrites for each texture that is changed. This is also the case for
FOMM managers from years back, albeit somewhat slower (Oblivion with Better Cities takes a solid 20 seconds even on a solid state).
Mods that contain scripts are handled on a per-save basis. Those scripts are run either at game launch, or while your save state is loading.
As for launching through NMM, this is optional. If you have special launchers like
SKSE (Skyrim script extender), or a 4GB patched executable for Skyrim 2011, it doesn't much matter. In my case, I changed my desktop shortcut to run the
SKSE launcher. Some major overhaul mods recommend that you launch through NMM, but truly, it doesn't matter for the most part.