i wanted to add also, im not sure if your faliliar with the process of them returning a child to the parent, but unfortunately i have been through it. in 2006 we became seperated from our 5yo daughter.
the system is quite organized. as soon as you realize your child is missing you let the closest cm know. for us it was coming out od philharmagic, so we told the fast pass attendant. he immediately radiod the lost child center. in the mean time my daughter had made her way to the tinkerbelle store and she told them there that she was lost. they only asked her for her first name, and then called the lost child center and found out where i was and they walked her to me. they wouldnt have gone through her clothing looking for id, it wasnt necsessary. nor would they have needed to call me on my cell, and to be honest i dont think they would have. i think they are trained to do it this way. possibly if the cm had called the lost child center and there wasnt a parent then they would have tried to find out more info, but i cant imagine a parent not looking for their child.
so anyway, i would make sure to tell the child to find the closest cm, theyre always in costume. or tell them to find the closest store. and then on your end find the closest cm and you will be reunited. i wouldnt go to the lost child center when you find them missing.