'Blackwater' refers to a type of naturally occurring water condition to which various tropical fish have adapted. It is typically very soft, acidic pH, high in tannins, but very low in contaminants. The water often appears 'lifeless', because of the relative absence of plant life in the water. This is due to the absence of mineral content in the water. Fish adapted to it are generally carnivores surviving on insect life, rather than herbivores. Fish from these conditions are usually extremely sensitive to nitrogenous contaminants. There are some beautiful African tetras that are extremely difficult to keep because even the best filtered aquarium cannot lower contaminants to a level necessary for the fish to survive long term.
Carp are very adaptable. I am sure they would live and reproduce in 'blackwater'... at least the ones that survived initially.

It is not, however, the water deemed best suited to koi. The soft waters of Niigata are wholly different, with pH seldom being below 6.8 in the data I have seen. In a 'blackwater' environment, a pH of 6.2 to 5.5 (and even lower) is more likely to be found. Niigata water is also free of tannins and such. Although the carp is very adaptable, keep in mind that nishikigoi were developed in Niigata and can be considered as being adapted to those water conditions through a few hundred years of selective breeding from ordinary food fish to what we prize today.