Is depression in a teenager curable by medication alone?

Not effectively. Both the tads and torida studies (depression treatment studies conducted by nimh) demonstrate maximum improvement in symptoms when medication is used in combination with cognitive behavioral therapy.
It depends. Some teens respond quite well to medications; others do well with talk therapy. Some need both, and even that may not be enough. An equally important question is what happens in the long term, and there the evidence is that addition of effective talk therapy can help prevent relapse and recurrences of depression.