I agree with the above, although Atilla's case would have been considerably helped by the fact that "By the time we had the appeal, as interventions were taking place, her problems lessened (although she was still not 100% back to normal) and we were able to present evidence that with proper intervention she can handle stress
all this being said, you need to determine if you feel she would be able to handle a grammar school. You know your child best. If you feel she can, then go for it. If you are unsure, get an opinion from a professional. If you know she is unlikely to handle it, then even though she is capable of grammar, it might not be the best place for her. better to grow up happy than stressed all of the time.
Another thing I would reccommend before going through with the appeal is talking to the SENCO at the grammar school to see how they handle children with anxiety issues. Some grammar schools will be great with it, others not very good. You want to make sure that if you do send her to a grammar school, you send her to one with staff who are understanding and experianced with this kind of situation.
Another good point - and I think an appeal panel would be impressed if you'd taken the trouble to seek reassurance from the SENCO.