You can appeal as Lougle quite rightly stated up thread regardless of whether you or school make the request, its just school that cannot appeal.
SENCO might be expecting for SA to be refused and for you to leave it there.
If you don't trust school, particularly if you don't feel they understand his needs, do it yourself, but do ask school to write a letter supporting your request, just makes it harder for them to back track at a later date.
If you are fully expecting SA to be refused, regardless of who makes the request, im wondering if it might be quite strategic to let school make the request, then you appeal the refusal.
This way they would have to explain to a Tribunal why they have changed their minds, if they do not support you at Tribunal.
Although saying that a letter in agreement with you request and supporting it, would do the same thing. Sorry im just thinking out loud!
Do it yourself! with the schools support and agreement!