Do you mean Statement of SEN (if you are in NI) or the SEN register?
Being added to the SEN register means the pupil needs additional SEN support, which sounds accurate from your posts. It isn’t just about academic ability. Some DC who are able are on the SEN register. Being added doesn’t result in social isolation. Being on the SEN register alone won’t result in someone attending a special school. It doesn’t prevent you applying to grammar. Some independent schools will ask you to declare any SEN, but that will apply whether DS is on the SEN register or not. Some independent schools are more supportive of pupils with SEN than others.
If you are in NI and mean a statement, that is for DC who need more support that can typically be provided in at a school level. It is a legal document that sets out a child’s needs, the provision they require and the placement (including a special school if required) they will attend. For schools that aren’t independent there are limited reasons the EA can refuse to name your preference. For independent schools there are slightly different rules.
A t-score of 62 would be above average. Are you sure it is a T-score?