Carbon-aware schedulers aim to reduce the operational carbon footprint of data centers by running flexible workloads during periods of low carbon intensity. Most schedulers treat workloads as single monolithic tasks, ignoring that many jobs, like video encoding or offline inference, consist of smaller tasks with specific dependencies and resource needs; however, knowledge of this structure enables opportunities for greater carbon efficiency. We quantify the maximum benefit of a dependency-aware approach for batch workloads. We model the problem as a flexible job-shop scheduling variant and use an offline solver to compute upper bounds on carbon and energy savings. Results show up to $25\%$ lower carbon emissions on average without increasing the optimal makespan (total job completion time) compared to a makespan-only baseline. Although in heterogeneous server setup, these schedules may use more energy than energy-optimal ones. Our results also show that allowing twice the optimal makespan nearly doubles the carbon savings, underscoring the tension between carbon, energy, and makespan. We also highlight key factors such as job structure and server count influence the achievable carbon reductions.