The verification and validation process of Drag-Free Attitude Control Systems (DFACS) accounts for the majority of the overall time and costs in the development of current space missions. Showing robustness of the system against uncertainties constitutes a key aspect in this process. This paper presents a probabilistic robustness analysis approach that employs a linear fractional transformation based polynomial chaos expansion. In this approach, a surrogate model is obtained that is used to verify DFACS performance metrics against given requirements in the presence of uncertainties. This approach is compared to the default one in industry, which relies on large-scale simulation-based Monte Carlo campaigns. A high-fidelity DFACS benchmark derived from a challenging real-world mission such as the Laser Interferometer Space Antenna mission is used as an application case. The results on a realistic mission scenario show that this alternative probabilistic robustness analysis offers computational efficiency when compared to Monte Carlo. The Monte Carlo results can be faithfully reproduced at a fraction of the computational time, offering a promising alternative to complement the industrial verification and validation process.