The effect of turbulent fluctuations on the transport of neutral particles (atoms, molecules) in tokamak plasmas is investigated with the 3D global turbulence code TOKAM3X-EIRENE in limiter geometry. The statistical properties of turbulent fields relevant to this work are discussed, including the recycling flux. The neutral particle transport is recalculated on the mean field plasma, and compared to the mean neutral particle density/flows obtained from the turbulent simulation, so as to assess the effects of the fluctuations, in particular on the ionization balance. The latter effects are remarkably modest in the simulation presented here, but are expected to become more and more pronounced as the high recycling regime is approached, in particular because the plasma temperature becomes low enough so that ionization is strongly non-linear. However, the turbulent fluctuations in the SOL do have a substantial effect on the neutral densities on the low field side of the limiter, including in the confined plasma. These effects are traced back to non-linearities in the plasma flux at the wall, and the fluctuations in the latter are identified as an important contributor both to neutral particle density fluctuations and to deviations from mean neutral particle density/flows in the turbulent simulation with respect to the same quantities recalculated on the mean plasma fields.