Yes there will be software API calls to "shut off" mono. We might use the term "sleep" or "hibernate" though.
In the lowest power mode, mono can only be woken by the reset switch or the user button. That is the closest to "power off" as you can get on Mono.
Will there be software shut off? If not then your comparison to smartphones is invalid, since they can be turned off.
Also many smartphones do have removable battery, I would never consider one with non-removable battery.