Yep, that should be possible and does not require a router. I would think it is significantly less low-friction than native Airdrop for a firefighter on mission though...
It could have an option to create a hidden hotspot and have the other phone also be able to discover the hotspot automatically (app specific SSID name is searched for and if user is not already in wifi, and hidden hotspot doesn't exist, then it will be created for the duration of transfer). Airdrop doesn't seem too different.
A hotspot requires a cellular connection to an existing network. AirDrop creates a ZeroConf network, which advertises its presence to other devices.
a hotspot that provides internet requires a cellular connection, you can still just make a hotspot that has not internet connection and acts as a regular lan