Imagine having a porsche in your driveway, but for reasons you can only use the first gear. No matter how hard you push the pedal to the metal, you won't be as fast as you want the car to go. Plus if you keep going full throttle in the first gear eventually you'll break something.
Sounds depressing, doesn't it? And that's exactly what happens. People eventually get depressed. It won't go away by itself. When they go to the doctor, it's basically a game of chance. If the doctor is competent, he'll do the proper tests. Unfortunately most aren't. There are a lot of syndromes, illnesses, conditions that match the symptoms.
If the ADD patient is lucky, the correct diagnosis is made. If unlucky, he may be treated for borderline, depressions, etc. Antidepressants may worsen the condition, because they may increase motivation without increasing ability.
A well diagnosed and medicated ADD patient however will lose depression in almost no time.