We have calculated cross-sections and rate constants for the title reaction by using the quasiclassical trajectory method and a recently reported two-valued energy-switching potential energy surface for the water molecule. By varying the amplitude and rate of decay of a local Gaussian term which controls the appearance of a barrier along the C-2x minimum energy profile, an attempt has been made to answer the title issue. A comparison of the calculated rate constants with the available experimental data suggests that the barrier, if existing, lies below the energy of the reactants, and separates the small van der Waals well from the deep chemical one at short distances.