Hole doping can control the conductivity of diamond either through boron substitution, or carrier accumulation in a field-effect transistor. In this work, we combine the two methods to investigate the insulator-to-metal transition at the surface of nanocrystalline diamond films. The finite boron doping strongly increases the maximum hole density which can be induced electrostatically with respect to intrinsic diamond. The ionic gate pushes the conductivity of the film surface away from the variable-range hopping regime and into the quantum critical regime. However, the combination of the strong intrinsic surface disorder due to a non-negligible surface roughness, and the introduction of extra scattering centers by the ionic gate, prevents the surface accumulation layer to reach the metallic regime.