I would think that they would not intend for the child to wait to eat until everyone else was served...if that's what the OP's preference is, then the child probably would have cold food.
All I know is that there was an adult who posted once that they did not want anything to eat at Garden Grill but the rest of the family wanted to go, and she wanted to know if she could purchase CS from Sunshine Seasons and bring it in for her as her meal. She called Garden Grill and asked, and the answer was "no." A couple of points about the previous inquiry: 1) the person who was to eat the CS food was an adult, not a small child. 2) Garden Grill is a family style all you can eat restaurant. I would think there MIGHT be possibly more leniency from an a la carte restaurant than from a buffet or all you can eat family style place.
Any reason you can't feed the child at a CS before entering the restaurant, then get the kid just a drink or fruit or a little mac and cheese or something? If the child is under 3 you will not be obligated to purchase anything for them even at a buffet/family style.