Actually, I think that the opposite might be true – the students coming from non-stressful, non-competitive high schools might have stronger reserves in terms of mental health than the ones from the high-stress high schools.
To start with, long-term stress has a biological effect on body and mind, due to production of stress hormones – and anxiety about grades and college admissions are a primary source of stress for teenagers. See: http://www.apa.org/helpcenter/stress-teens.aspx
Students at less competitive high schools may also benefit in other ways that help them cope with college. If their high schools encourage collaboration and cooperation rather than competition, they may develop interpersonal skills that serve them well in a demanding college environment. For example, they may be more prone to form and participate in study groups and work cooperatively with fellow students, rather than a go-it-alone approach all the way through.
Students from less competitive high schools might also have less of their egos or sense of self-worth caught up in their grades, perhaps coming from an environment where less importance was placed on GPA. They may have stronger reserves of self-confidence, simply because they come from an environment which reinforced rather than challenged their sense of competence and ability to succeed. They also may have developed life habits that are more balanced, with appropriate time for recreation, socializing, exercise, and sleep — which help them weather life stresses later on. They may simply be served by a more relaxed attitude overall and an ability to take their day-to-day college experience a little less seriously — after all, it’s not the end of the world to get a C in a class.
And they may simply arrive at college with more energy and enthusiasm, simply because they don’t feel burnt out and exhausted from their high school experience.
Of course, this is all a generalization, but I am responding to a comment that is also based on generalization – and as a parent, I very specifically avoided placing my kids in high stress elementary & high school environments. I wanted my kids to learn, but I wanted them to do so in developmentally appropriate settings, with plenty of opportunities to develop an array of life skills in addition to academics. I wanted my kids to enjoy life and have fun as teenagers, and to enjoy the social aspects of their high school years.
I’d add that not all kids coming from less academically challenging high schools are coming from stress-free environments. There may be all sorts of intense stressors both at school and at home for students from different walks of life, which go far beyond worrying about studying and grades. And the students who come out of those stressful environments may have a higher level of resiliency and a broader sense of perspective than more privileged kids coming from academically challenging high schools, but otherwise very sheltered life environments.
So no, I wouldn’t predict doom & gloom for students for the middle class and lower-middle class students that Chicago now says it wants to attract.