Suppose I'm speaking to waitstaff at a restaurant explaining that a diner in our party has an allergy. When speaking to someone working at the restaurant, would it be appropriate to refer to such a person as お客様 (seeing as the person is not actually my customer), or should they simply be referred to as こちら?
No, it would be weird to refer to your own party as お客様 as it implies it is your customer in that context (so only the waitstaff would use it). Generally, you don't use 尊敬語 to your "own side". That said if you need to honor the person (e.g. it is your client), then I would use こちらの方.