Yes.
I just skimmed the readme. It states a "local network" multiple times. So in this example, the firefighters need a Wifi network to connect the devices. Not because the files are sent over the internet, but because LocalSend doesn't create an ad-hoc network unlike to Airdrop.
So OP: technically yes, but the experience is not quite the same.
Then you could have the fire-trucks mesh network with each other!
Sarcasm alert: I'm sure that is bound to be 100% reliable out in the middle of nowhere, with whatever cheap power converter they used to provide power from the 12V batteries in the truck, and hopefully doesn't drain them :)
https://developer.android.com/develop/connectivity/wifi/loca...