The fueling efficiency of supersonic molecular beam injection (SMBI) depends on injection parameters. In this article, we report on simulations of SMBI into turbulent edge fusion plasmas. Density continuity equations, which describe the dynamics of molecules and Franck-Condon atoms, are coupled with the plasma equations in the hot-edge-sol-electrostatic (HESEL) drift-fluid model. Numerical simulations, with parameters relevant to experimental conditions, are performed in order to investigate the dependency of the fueling efficiency of SMBI on the molecular beam density, velocity, and beam width. In all conditions, the efficiency grows with the increase in the molecular beam velocity. The variation in efficiency with respect to the beam density depends on the plasma pressure and the ratio of the density source, produced by ionization of neutrals, to the plasma density source provided by core fueling. The effect of the molecular beam width is pronounced only if the beam density is high and the plasma, into which the beam is injected, is relatively dense and hot. The influence of plasma fluctuations on SMBI is weak; however, a strong neutral injection leads to suppression of a turbulence transport due to relaxation of pressure gradient profiles.