I cannot speak from experience, but I highly doubt the servers are going to ask your child's age. My guess would be if you were trying to order from the children's menu they would say no, but a 10 yr old ordering from the kid's menu and I can't imagine they would say no.
I also feel it is completely ridiculous for Disney to consider a 10 yr old an adult for dining purposes. My 10 yr old DS does not eat nearly the amount that I or my DH do.