I presume there must be plenty of protections for such a case, but is there any reason to be concerned if I turn off (or my fortrezz value and smartthings turns off) my main water supply and my Rinnai tankless isn't turned off? I looked at the instruction manual and it doesn't mention any thing about this situation that I saw.
Tankless/combi just won't start if there's not enough flow (it's well written on tech label), usually minimum flow that let fire light is around 2L/min, that's intrinsic in their way of work. Most use a microswitch to sense the flow and a temp. sensor to adjust the flame, other just measure the flow and adjust the flame according to that. Some have minimum pressure sensor, other do not but on DHW it's not needed.
There are flow sensors in tankless units so if you are simply shutting down the valve on the water supply and then reopening it I wouldn't be too concerned. That being said shutting down the water supply can change the pressure in the system as temperatures of the water change. I don't think it would cause any trouble. But, anytime you close the valve the water is in a closed system. It's a good idea to install a potable water expansion tank.
They are almost exclusively 3/4" NPT. You would need to measure your static pressure(pressure with the taps closed and the main open) with a gauge. Then pump air into the air nipple (bottom of the tank pictured above) with a bicycle pump or preferably air compressor to match the static pressure before installing it. It's a good idea to install a service valve as well.