Disney started modeling CRO after other call centers over a year ago. CMs are required to give you "the 3rd degree" for call quality monitoring purposes; calls are recorded and scored against a checklist of over 30 points the CMs must cover on every call. Imagine trying to do everything on the checklist whilst being friendly and giving out information at the same time- not easy, especially when you're being required to work 60 hours a week tied to a phone.
That being said, you could probably nicely tell the CM that, while you know they're requred to ask you for this information, you'd really prefer not to give it until you know if the codes are out or not. Most CMs will then feel that you've gotten them off the call monitoring hook and go right to the info.
But ALWAYS give your info up front if there's ANY chance you might book a ressie; the reservation/availability program launces from the database, but is a totally separate program. If you don't give your info and try to book, adding your info manually into the res program takes much, much longer than giving it at the call start.