First we don't know which species of ant you mean by "common" black ant. The black ant that is common in your area may not be the same as the black one that is common in another area, but some ants do attack termites, and depending on the outcome of the invasion and battles the termites might be eradicated. The termites don't always lose the wars, they have some formidible soldiers of their own, and can destroy the ant nests.The ants that attack, and are attacked by, termites can be loosely grouped into two groups; those that are carnivorous [or myrmecophagous (ant eating) or formivorous (termite eating)] and prey on the termites; the other group would be ones that compete with the termites for the same food. In the first group are some ants that are black and common. Today the most important ant in the first group in many areas is the imported fire ant which has pretty much wiped out or at least suppressed the "common black ant." There are also some domestic fire ants. They will raid termite nests for food and if the raid is severe enough can wipe out the termites. In the competitor group (termites eat other vegetable matter besides wood, dry grass and seeds for example) are some other ants that are black and common; the harvester ants( there are red types and black types) that collect vegetable matter to grow their main food, fungus; and some others that feed directly on the vegetable matter just like the termites. And of course the carpenter ant that specializes in wood, it is a black ant but is very large and not one that is called 'common.' Most of the battles and war don't result in the eradication of either colony. If the damage is severe enough or goes on long enough one or the other colony may relocate, usually not far enough away to make much difference to you in the case of the termites And having the termites replaced by carpenter ants wouldn't do you much good. Replacing termites with fire ants raises a ahole crop of other problems.

Ant's are the 1 predator to termite colonies. They will not eradicate the infestation.

no, a common black ant wont but the much larger carpenter ant can and will erradicate the termites, problem is the carpenter ant will take up residence in termite colony and while they do not eat wood they will, over a period of many years, since the colonies survive a very long time, tunnel out more room to live. so its a double edged sword. and there is no guarantee the carpenter ants will win