Secure exams is a big topic among the teachers I work with too. Yes, MoodleBox is a portable examination environment too! May be one could make it secure more easily than the usual Moodle LMSs in the wide net.
Interesting, we never thought of the candidates communicating with each other through their client devices, laptops in our case. You know that the number of simultaneous clients is limited by the RPi hardware? From what I read the number is about 20. Since they are physically in an examination hall and the number is small, invigilation is doable and simpler than technical means, I would say. Our people look for unattended (no invigilators) because of the large classes.
Anyway, the NixOS woke my curiosity. I've never heard of it, otherwise an old distro-hopper. Could you explain the client setup a bit: Is the NixOS a VM? Why NixOS? What is the programming environment they need to install?