Yes, I record all children with/without diagnosis and those that have received support in the past. I highlight these as ‘monitoring’ as they aren’t receiving current additional support, but it’s important to be aware of them and their possible needs.
This works for me, but I do work in a small school.
I still think you need to find your own way of recording the register that suits you, but all those receiving support above QFT should def be on the register 👍🏼