Makes sense if the drawers completely fill the volume of the fridge, so most of the air is inside the drawers and there is minimal air loss when the door opens. If the drawer fronts were insulated, each drawer would effectively be its own chest.

Edit: On a reread, I'm guessing you were talking about individual refrigerated drawers? Multiple drawers in a single insulated box (as I interpreted it) could work though, as it would have less exterior surface area, use less insulation for the same thermal resistance and useable volume and have a single cooling unit, which might be more efficient. It would also fit existing fridge alcoves.