Even if they did (and legally, parents have to be allowed to state their reasons for naming a school as a preference), unless the school in question has an oversubscription criterion including the situation - 'exceptional medical / social' might, but by no means all schools include this criterion in their admissions policy - no notice would be taken of it when ranking the application.
And if the school did have such a criterion firstly, evidence as to why only this school, on those grounds would have had to be submitted at the time of application and secondly, whoever assesses the information provided by the parent and their supplementary evidence woukd have to agree that the application met the standard to be ranked under that criterion.
School applications can only be considered under the published admissions criteria for a school, and on information known to the admission authority (be it LA / governing body or whatever) at the time of application. At appeal, issues influencing the parents wish for a school place, which are not covered by the school's published criteria, can be and will be considered.
(However - just like a school now being said to be totally unsuitable, based on a situation which already obtained at the time of application, turning out to have been e.g. second preference on the appellant’s CAF - not having mentioned something already known to the parent to be vitally important, and the school in question having a relevant criterion, only mentioning it at appeal, might also not unnaturally cause a bit of a sideways glance, so to speak).