Is it possible to change the plugin folder location?

Sure thing. There are two options here:

One is that you can start QGIS with the --configpath arg so that all the configuration including plugins are stored at a custom path. Like so:

qgis.bat --configpath "D:\{somepath}"

You can put that in a .bat file and get the students to launch that.

This also has the advantage of being able to run QGIS, set it up how you like it, install some plugins, then just move the whole D:\{somepath} to a new home e.g. each machines D:\ so that each student has the same setup.

OR

You can set the QGIS_PLUGINPATH variable before you load QGIS which will tell QGIS to load extra plugins from that path. Like:

set QGIS_PLUGINPATH = D:\{somepath}

However with QGIS_PLUGINPATH QGIS will still install into the users home folder on the main drive (C:)

In QGIS 3:

Navigate "Settings > Options > System", go to "Environment", check "use custom variables"(1) and add a new variable(2) as following:

(3) Append, QGIS_PLUGINPATH, 'C:\PathToYourPlugin'