The low-flush toilets are better than the older models because they don't flush all of the water out of the bowl - they use the height of the water in the tank to help with the pressure, but stop before it is empty. This means that the cold incoming water is first mixed with the (probably ) warmer water there, and second, not as much is there, so it may contain water that has been tempered somewhat from being stored inside. But, if you have a marathon series of bathroom breaks, the water in the lines and the water stored in the tank will get the full cold water shot, and probably will cause it to sweat. Keep in mind too that insulation just slows the transfer of heat - flush the toilet often enough and the tank wil still get cold enough to sweat.
Can't comment directly on the Drake...my mother has two in the house, no a/c, and I've not noticed any problems, but I'm not there very often.