I agree with what most people have said; if he does not need any additional intervention at school then under the CoP technically he doesn’t need to be on the SEN Register.
However, with students like this I have an ‘additional needs’ register where I keep people that I need to monitor; this means that I am ready to swoop in if that need level changes. Additional needs children have a teaching and learning profile with a brief summary of what we know and flagging potential risks to progress or wellbeing. There are strategies for teachers if they need. I tend to review the profiles each year to make sure that the information is up-to-date and throughout the year I have an excel spreadsheet to jot down anything that I hear in the staff room, in school reports, in pastoral meetings etc just in case there are early signs of an escalation of needs.
It helps parents if there is another step between ‘on the register / not on the register’ so that they feel that their child won’t be missed or forgotten and gives you peace of mind that you have ‘something’ in place.