Don't know, but I don't think so. One saving feature, though, is that since the toilet does not use much water, and it doesn't dump all of the water that is in the tank, the incoming water will mix with what is likely warmer water, and may not be above the dew point. Also, since it doesn't use as much water per flush, depending on how long the supply pipe is, that water may be warmer than when it had to fill the tank with 2-4x as much water, it may not get the cold stuff to the toilet.
None of this will make a difference if you have a marathon parade to the toilet, though...you'll run enough water to get it cold.