May or may not be directly affiliated with the Ministry of Magic. Lockhart was an honorary member (CS6, GF31, Pm). One of the members was interviewed for an article of Rita Skeeter’s, where he expressed prejudices against Parselmouths (GF31).
The name is rather odd, as it implies a defense of Dark Arts, rather than defense against them. But the remarks in Rita Skeeter's article are solid evidence that the League is, at least on the surface, against the Dark Arts.