In LEO it doesn't need to be rad hardended, especially for something that isn't life critical (compared to say, the control system of a space shuttle). At this altitude, the atmosphere and magnetic field provides a lot of protection still.
At the very least SpaceX would test the devices to see what effects the higher radiation would have. However it's not unreasonable to just have the software detect and reset itself, if a high energy event is detected. There are going to be a lot of these satellites and a lot of redundancy in coverage, so if one is down for a few minutes it's not that big of a deal.
Yes, as long as radiation only causes upsets and not permanent failures — satellites are somewhat expensive — and as long as software can detect faults and reset.
Sure, but that isn't saying an awful lot; most satellites are very expensive. SpaceX would want to weigh the cost of hardening the system against radiation versus the cost of another launch to replace failure(s). I'd guess radiation-hardening of some kind (at least sufficient to prevent most permanent damage) would win out in that calculation, but I'll happily admit I don't have any particular factual basis for that guess.
At the very least SpaceX would test the devices to see what effects the higher radiation would have. However it's not unreasonable to just have the software detect and reset itself, if a high energy event is detected. There are going to be a lot of these satellites and a lot of redundancy in coverage, so if one is down for a few minutes it's not that big of a deal.