The host has a bunch of functions. One is to apply the forward error correction to the incoming data before its retransmitted.
It's also sets up the time sync to define the timeslots for the subscribers. It's not just getting data to flow from one radio to the other. The software running on the computer or Pi does all this using the modem.
In a way, the radios interact with the repeater, beyond just keying up like a conventional P25 radio, or a NXDN radio because the DMR radios are using TDMA.
When you press the PTT, the radio sends a series of wake up packets to the repeater, and is expecting a specific response from the repeater, before the radio begins sending data. Also keep in mind,
Could it be done by an arduino? Maybe? I don't know.