The education-in-a-suitcase system being presented in Maseno is pretty robust and a short power failure would have gone completely unnoticed if the projector had not been turned off! All the components run off batteries so the whole system just kept on chugging away.
But one can do much more serious tests and just for the heck of it we tried a whole suite during the workshop. First, after logging into the (portable) server (and getting questions+syncing answers) we tested turning off the WiFi. That has no real effect on anything since the questions have been loaded into the tablet and the students simply keep on working. Next one tries to shut down Chrome. Again, when Chrome restarts, it finds the pages in exactly the same shape as when it was shut down. Finally, shutting down the tablet completely and rebooting again brings up Chrome in the same state as before with nothing lost.
Of course after working offline the student has to connect to the server at some stage to upload the grades. This is pretty trivial — just get the tablet back into WiFi contact with the laptop and either request a sync or ask for+answer a new question. The server then asks you to login again and starts syncing after login. 
Whether the laptop server has an Internet connection or not through its sim card similarly has no effect at all on the student -- unless the student happens to be browsing Facebook instead of studying :-)