Dear In Turmoil
I'm afraid it's not possible to say whether you have enough evidence because it depends how strong a case the LA puts forward on behalf of the school to resist further admissions, and how strong the other appellants' cases are.
However, I would advise you not to use the letter because it looks as if it could be a serious breach of the Code of Practice:
2.15 Representatives of the schools being appealed for must not support individual appeals at
the hearing itself or by providing letters of support for appellants, because of possible
conflicts of interest and the possibility of unfairness to other appellants.
It wouldn't, of course, be your fault if the letter were deemed inadmissible, but any suggestion of "favouritism" on the part of the school is unlikely to assist your case.