How do wi-fi only Android devices synchronise time?
We confirmed with the device manufacturer that the devices use NTP to sync the time with pool.ntp.org. After a bit of research of my own, I discovered that NTP is configured in /system/etc/gps.conf. You have to be root to edit this file, but I was at least able to confirm that the information given to us was correct.

We have opened the firewall to traffic going to pool.ntp.org, and so far all of the devices have kept in sync, so it looks like this has worked as intended.

Thanks to http://forum.xda-developers.com/showthread.php?t=1200089 for the info on the NTP config file.