We used a stochastic 3D pore-scale simulation approach to statistically elucidate the effect of stochastic pore connectivity on permeability and hydraulic tortuosity of highly heterogeneous porous media such as carbonate rocks. The novel nature of our workflow lies in the generation of multiple 3D pore microstructures of the same effective porosity, pore size distribution, number of pores, but different stochastic pore connectivity where the only pore microstructural feature changing is pore connectivity. This workflow allows the explicit study of the role pore connectivity plays in permeability and hydraulic tortuosity without the interference of other pore microstructural factors or noise. Permeability and hydraulic tortuosity of the 3D pore microstructures of the aforementioned characteristics was obtained from direct pore-scale simulations using STAR CCM+. Our approach suppresses the necessity of conducting hundreds of experimental measurements and allows the training of neural network models to predict permeability and hydraulic tortuosity. We show that an approximate twofold increase in heterogeneity (pore size standard deviation), results in a two orders of magnitude reduction in permeability, and that an increase in heterogeneity results in a systematic shift of permeability from normal distribution to lognormal distribution. While the stochastic connectivity of pores has a significant impact on permeability, it has only minimal effect on hydraulic tortuosity. Furthermore, the predictability of permeability from hydraulic tortuosity decreases with an increasing heterogeneity. The high coefficient of determination obtained in permeability prediction with a feedforward neural network (NN) model trained with of PTSD data along with pore surface area parameters indicates that NN algorithms can capture the effect of stochastic pore connectivity on permeability. Since PTSD data and surface parameters can be obtained from mercury injection capillary pressure (MICP) measurements, our findings have large implication toward the prediction of permeability and hydraulic tortuosity in highly heterogeneous porous media.