I am also familiar with the organization and this event as it happens every year at my local high schools as well. But, it's not generally considered a school club or organization as it tends to be student run and led, and not a regular event sponsored by the school or using facilities at the school.
The problem is that given the language of the EAA many schools interpret it to mean that there can be no monitor or sponsor who is a school employee. And, if they have rules that require a teacher or staffer direct, participate, or at least coordinate/permit access to school facilities for the organization then they are violating the EAA. In an effort to forestall any arguments on what is or is not considered participation by the school, many have opted to either prohibit ANY activity that might be seen as having a religious component (even if they are inclusive and/or not mandating any acts of faith at the meetings including YMCA, Boy Scouts, Young Life, or Friday Night Live, and others), or, to ban any organizations not directly related to a sanctioned and legitimate school activity (sports, math, science, etc.).
We have school groups that meet off campus at church facilities because the local schools have opted to err on the side of extreme caution. As a result, though, these off-site meetings often DO have the participation of school staff and teachers.

