I think it is around 100c but no it shouldn't run with the engine off and the ignition on unless it is at 100c of course.
My Triumph Daytona 955i does this, I'm yet to investigate but that bike doesn't have a relay for the fan and so if it is not the temp sender it is most likely the ECU...
I don't know if the SRAD'S fans runs direct from the ECU or if they have a relay, you'll probably be fine as the reliability on these is so good.