My big question would be: "For the sake of what?"
As a physician I was taught never to order a test unless I knew what I would do differently with the results. I tend to side with Nadine Burke Harris (you can watch her TED talk, read her book) that ACE screening doesn't belong in schools. We don't need to know what is happening...we do need to know how to respond to every child. Knowing their ACE scores doesn't change our behavior. We still need to build classroom communities. We still need to put routines in place, teach self regulation, mistakes are opportunities to learn and teach ourselves and our students how to respect each other in all our uniquenesses.
We have been implementing trauma informed practices in schools for 10 years and I think it can be done really well without any knowledge of a child's ACE score. (And it is a better practice for learning communities including for kids with ACE scores of zero).