Yes, schools should screen children and teenagers for signs of mental illness and suicide, because if children can be treated early, it can make a big difference. Treating a mental illness when young is a good way to make someone happier as an adult. Illnesses are easier to treat when young. This would be a good use of school time.
No! Mental illness is not something that can be physically observed like a broken bone or a bacterial infection. There is no one-size-fits all diagnostic criteria and diagnosises can vary from one doctor to the next. If schools screened kids, it could lead to unnecessary or even invalid labels, medications, etc. sometimes it's difficult do differentiate lack of discipline from mood and behavioral disorders.
When my son was in kindergarten he had a lot of energy and had a hard time focusing in class. The school requested we take him to the doctor. Over the course of a year, he was first diagnosed with ADHD and medicated. He started sleep walking, wetting the bed and lost weight. Another doctor diagnosed him with oppositional defiance disorder and bipolar disorder and hooked us up with a new set of medications. A third doctor said, "show me a five year old boy that can sit still and be perfect in class. There's nothing wrong with him." He's been off all Meds now for three years and has matured. Problem solved. He needed discipline.
Two years ago my oldest daughter cut her wrists an showed her nurse at school. They called some kind of response team to evaluate her and offer guidance. They talked to her for 15 minutes, interviewed us and then told us she had borderline personality disorder! They told us we needed to get her help right away and that they'd follow up with us. We took her home and searched her room. We took her razor and told her we felt she was too immature to shave. At dinner she wasn't allowed to cut her own food. We did it for her like she was a baby. We talked about effective communication strategies, made her write five pages of other, positive things she could have done if she was upset, sad or wanting attention and told her if she ever did it again she would have to stay in a mental hospital. She never did it again and she is now very into sports and finishing her sophomore year on honor roll.
If schools starting screening kids I'd homeschool my kids. Kids go through rough patches and are constantly changing. People need to accept that there's not something wrong with everyone. People are too quick to blame misbehavior on a disorder. I don't feel parents take enough responsibilty for their children any more. Know your kids. Know when something isn't right.
Schools do not, and should not, require any medical testing for students. Let's say a child did have mental illness. Does that mean the child should not be educated? Of course not. Schools has a right to some medical issues, those that are contagious for example. Measles and chicken pox vaccines must be given to school children of a certain age to avoid outbreaks, as they are highly transmittable. That makes sense. Depression, however, is not contagious. If anything, a school or teacher should notify a child's parents if they truly are educated enough on the subject to see cause for concern.