I think teen depression, is a wonderful idea! In today's society it does not matter what age you are but teens are in a catergory where bullying, image, and other things are at the fore front and they have to deal with peer pressure, depression is there for teens as well, so I think this is a great idea.
I think that having teen depression screening in schools can be good if they are allowing the children to express why they are depressed and will be helped to fix the situation. Also this will allow the parents to know what is going on with their child and be able to build them up and help them out of their depression.
There are complications that could come up. Maybe the teenager says things to the questioner that indicate depression only because they are using emotional terminology in an atypical fashion (i.E. They use words like "depressed" when really they are just sad) for what ever reason. Co-screening with alexithymia (which makes identifying your emotions difficult) and autism (where you may not know how to communicate your emotions) may help. Questions about recent events such as deaths in the family should also be asked so grief is not mistaken for depression. Questions about breakups and academic performance (particularly recently but relative to how it was before) would also be necessary. That probably isn't even enough questions.
There are a number of things that can throw a person off of what is typical for that person, and misdiagnosis is likely to happen when a psychiatrist assumes that the person is behaving the way they usually do. For this reasons repeated screenings is a good idea. Assuming that how a person feels at one point in time is going to be the same as how they feel later is invalid. Circumstances effect how people feel.
Worrying if everyone will find out. I am a teen who currently struggles with depression. I am getting through it on my own. I don't need any help or assistance. Most people don't even know how to act around depressed people. Most of the time, they make us feel worse. "Just feel happy, focus on the good stuff" advice from a trusted adult I went to. They made everything so much worse than it was. There are more examples. Finally, I just gave up and decided that I would be my own hero. I have gotten much better since I started relying on only myself.