Block ice is used to slow the temperature drop rate. Cube ice has such a large surface area that it can kill the fish. The temp can drop so fast with cubed ice, the fish have no time to acclimate. A little dechlorinator is always a good idea with ice, regardless of the water source.
That's interesting Rex. I have dumped in the bag ice from gas station/convenience stores for years and never had a problem. All the ice producers I know remove the chlorine/chloromine before making the ice. They have special filters that also make it as clear as possible.
According to the literature I have about adding municipal water to recirculating systems that had chlorine in it, as long as it is 10 percent or less of the volume of the system it's not a problem.