This is a question with an extremely complicated answer. The success rate will vary based on the etiology or cause of the language disorder. As language disorders may be caused by many different conditions including deafness, childhood apraxia of speech, auditory processing disorder, oral motor difficulties, and more, the treatment and efficacy will vary. Also, the definition of "success" must be defined. One person may define success as a child reaching the level of their peers without a language disorder. Another person might define success as a child making greater progress with therapy than they would make without therapy, and by making substantial gains in the ability to communicate via alternate methods if verbal communication is not possible.
Early intervention is nearly always critical for young children with a language disorder, no matter the etiology, to make progress. The earlier intervention can take place, the greater the potential gains due to the neuroplasticity of young children.