You do realize that is a cloudy argument because there are numerous people without diagnosed disabilities in those schools. For example, when integration happened in schools there was an alarming number of African American students suddenly enrolled in special education. It also doesn't always require a physician to enroll these individuals in schools.
Also most in most of these shootings, it's usually implied after the fact that they probably had mental illness. Look at Dylan klebold, the Littleton shooter, the uni bomber, Dennis rader, and many others. Mental illness diagnosis and gun control are not cut and dry as many people seem to think