The objective of the Optimal Transmission Switching (OTS) problem is to identify a topology of the power grid that minimizes the total energy production costs, while satisfying the operational and physical constraints of the power system. The problem is formulated as a non-convex mixed-integer nonlinear program, which poses extraordinary computational challenges. A common approach to solve the OTS problem is to replace its non-convex non-linear constraints with some linear constraints that turn the original problem into a mixed-integer linear programming, named DC OTS. Although there is plenty of work studying solution methods for the DC OTS in the literature, whether and how solutions of the DC OTS are actually useful for the original OTS problem is often overlooked. In this work, we investigate to what extent DC OTS solutions can be used as a fast heuristic to compute feasible solutions for the original OTS problem. Computational experiments on a set of PGLib benchmark instances highlighted that the optimal solution of the DC OTS is rarely feasible for the original OTS problem, which is consistent with the literature. However, we also find that easy-to-implement modifications of the solution procedure help to address this issue. Therefore, we suggest using DC OTS solutions as a complementary option to state-of-the-art heuristics to compute feasible solutions of the original OTS problem.