Actually it's both. It's a disease (like any other addiction) in that it is treatable and curable (And unlike other addictions, contagious). Most addictions are not curable until the patient realizes he's sick. Once someone realizes that he has SAD he is easily cured.
Now since the SIN is the behavior of homosexuality and not the mere tendency to it someone can suffer the disease but never act on it and they are sick but sin-free.
Likewise an alcoholic is not sinful until he surrenders to his disease and drinks (to the point of drunkeness and beyond). He has the tendency toward alcohol abuse but if he doesn't drink he doesn't sin.
I chose alcoholism as there is a certain genetic component to it so someone who has never drank can still be determined to be afflicted with the disease. 'Homosexuality' has no genetic component and therefore can't be detected except through the behavior, however, someone who doesn't practice the behavior can still have the disease and still needs to be cured of the underlying trauma that causes the disease (else a future outbreak may happen)