So I got curious and found
this article by Randy. In it he theorizes that it's mostly Magnesium Hydroxide that precipitates out.
Still, my Calcium Chloride consumption goes up relative to the amount of Sodium Carbonate I've used in my mix, so there must be some Calcium Carbonate. When I tried straight high density Sodium Carbonate it wasn't pretty! It coated the entire inside of my sump and return lines with Calcium Carbonate.