Cu2SnS3 is a promising absorber material that has attracted significant interest in recent years. However, similar to Cu2ZnSn(S, Se)(4) (CZTS), Cu2SnS3 displays cation disorder, which complicates the scientific understanding and technological applications of these materials. In this work, we use postdeposition annealing to convert disordered Cu2SnS3 thin films to the ordered structure. After annealing, we observe crystal structure changes and detect improvements in the majority carrier (hole) transport. However, when the minority carrier (electron) transport is investigated by using optical-pump terahertz-probe spectroscopy, minimal differences are observed in the lifetimes of the photoexcited charge carriers in the ordered and disordered Cu2SnS3. By combining the experimental data with theoretical results from first-principles calculations and Monte Carlo simulations, we are able to conclude that even ostensibly "ordered" Cu2SnS3 displays minority carrier transport properties corresponding to the disordered structure. Transmission electron microscopy investigations reveal only a very low density of planar defects (stacking faults and/or twins) in the annealed film, suggesting that these imperfections can dominate minority carrier transport even at low levels. The results of this study highlight some of the challenges in the development of Cu2SnS3-based photovoltaics and have implications for other disordered multinary semiconductors such as CZTS.