Getting your dessert "to go" is possible, because you can just tell your waiter/waitress you need a box. But getting it from the front desk when you're not there to eat first - that might not be so easy. There have been reports of people trying this and being told "no" because the check-in counter is not set up as a cash register to order foods, and the people working that area are not equipped to take orders, and cannot leave to go get food from the kitchen, so be prepared for a very possible "no" when you ask. Don't remember if it was specifically at the Brown Derby they got turned down or somewhere else, but I know I read that someone has tried to get a dessert to go this way -- I read a thread about that here on this board somewhere.
I would try at Starring Rolls. We've been there several times, but I don't actually remember seeing the grapefruit cake at Starring rolls. They may be able to go next door & get it for you - I think they actually share a kitchen there.