I'm assuming all locations have L2/L3 connectivity to each other (either via VPN or direct connected switches, etc)
Networking has little to do with 3CX as a phone system specifically. If your network can handle the load of 800 SIP devices (and with 5k PCs I would hope so), 3CX would not have an issue any more then Cisco, Avaya, etc. SIP is SIP and packets are packets. Ensure you have low loss and latency to provide a good experience, although this applies to everything.I'd also require a separate voice vlan at this scale - which I'm going to assume you already have.
Email and SMS for emergency alerts
-3CX is quite weak in this area. You can get an email containing what extension dialed an emergency number and that's it. Unless you add 3rd party tools, (for example:
https://www.voiptools.com/product/3cx-911-notifier-by-voiptools/ ) that's what you get. No school specific "lockdown message" showing on phones, no second call to designated extensions informing of this, and so forth. And no SMS at all - 3CX just doesn't have SMS support.
You can however use panic buttons provided those buttons can talk on an ATA or speak SIP directly, and you can configure those to go anywhere you want. That is more about the panic button though. It's just another "extension" and depending on the button options will depend on where it calls and what it says.
Camera feed integration - depends. It's possibly doable depending on the hardware used. Someone else might have more info on that.