Generally speaking, most plugins act like Dmitry says. Especially the python ones.
A few more specialist ones (including SACP) need 3rd party software and might require admin rights to install these dependencies, especially on Windows. There's a couple of stategies to consider which might make things easier:-
Option 1: Use a virtual machine
Would students be able to install something like VirtualBox? If so you could set up a standard QGIS desktop environment with all the required plugins, and give them all a ready-made environment with all tools, libraries and plugins ready-installed.
This would have the advantage (in a learning setting) of having everyone start with the same setup, and that they wouldn't be messing up their own install (e.g. if they have QGIS already).
The downside is the time required to set up the VM (although this is only done once, by you) and the fact that users may not be familiar with Linux - although something like Ubuntu would probably feel comfortable for windows users.
I use this to try out cutting-edge versions of QGIS without messing with my own install... if I really mess things up, I can clear out the VM and start from scratch.
Option2: GIS on a stick
There are also GIS-on-USB products out there (PortableGIS springs to mind). These tend not to be cutting-edge (they may be 2.x) and I'm not sure if they can be run solely from USB, but it's worth looking into.