Can't see why they would not work, the drops of rain are very small compared to cars so they can probably tell the difference. Though I guess heavy rain would probably blanket the radar and it would not "see" cars.
I wonder how those work for multi lane roads, wonder if someone passing you could end up with you getting the ticket, or if it knows which car that's going faster. I've heard horror stories of parked cars getting tickets from nearby red light cameras.
I recently got nailed by a portable speed trap, no ticket in the mail yet though. I totally forgot about a zone that got dropped from 60 to 50 and was doing 70. Oops. My fault, should pay more attention to my speed, and signs.