@ejolson is right, PiNet unfortunately is designed primarily for use on a single site/school. It doesn't include any built in methods for syncing users back and forth.
The entire system can run over an SSH console though, so if you had remote access to each site via SSH, you could manage it but would still be one server at a time.
As for network booting over the internet links to a single server, I would highly recommend against this. It is possible, but slow and unreliable in general from my own testing as the core components it is all built upon are designed for low latency environment.
As well, there are a number of flags enabled by default with PiNet (and LTSP in general) for favouring faster connections over stronger encryption, meaning the system shouldn't most certainly not be publicly accessible via the internet. Although a site-site VPN would be doing, as mentioned about it would be slow and unreliable.
Unfortunately I don't have a nice answer for you. Being able to centrally manage multiple PiNet servers (or share users between them) are both pretty low down on the priority list given the rather limited number of users it would benefit, so have to prioritise my limited time to work on PiNet on other features (like currently Stretch).
It is on the list though for someday
Lead developer of PiNet, a free and opensource centralised user accounts and file storage system for Raspberry Pi classrooms used in over 200 schools across the world.