Ordinarily someone who is not a member in good standing of an evangelical church should not participate in the Supper. The PCA Book of Church Order provides these two options, which are consistent with biblical teaching:

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Since, by our Lord's appointment, this Sacrament sets forth the Communion of Saints, the minister, at the discretion of the Session, before the observance begins, may either invite all those who profess the true religion, and are communicants in good standing in any evangelical church, to participate in the ordinance; or may invite those who have been approved by the Session, after having given indication of their desire to participate. It is proper also to give a special invitation to non-communicants to remain during the service.
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Anyway, salvation is ordinarily not possible outside of the visible church. God does not save us merely by joining the church, but salvation expresses itself in and through our participation in the visible church.

As to Seth's example, I think that the parents of the girl may be de facto members of the AOG church, even if the church does not officially recognize membership as a concept. In any event, I think the elders would have discretion to permit the girl to participate because of her special circumstances.

Scott

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Scott Roberts
Ruling Elder, Lakeside Presbyterian Church (PCA)
Southlake, Texas