Resonant Magnetic Perturbations (RMPs) and Advanced Divertors (ADs) are both promising candidates to be utilized to meet the challenges of power exhaust in future fusion devices. A combination of both approaches is a promising avenue in order to achieve a stable, high performance plasma edge in an integrated way that takes into account divertor heat load limits while allowing for density and impurity control. The latter is of particular importance in spherical tokamaks which feature Edge Localized Mode free high confinement H-mode regimes prone to density rises and core impurity accumulation. The capability to control core densities and particle exhaust in spherical tokamaks needs to be assessed to determine their viability for compact fusion nuclear science facilities. The experimentally observed, density pump-out effect induced by the application of small amplitude RMPs is an important phenomena with respect to density control but its underlying cause is not well understood. One proposed mechanism for this density pump-out is that the opening of formerly confined field lines from the plasma edge enables enhanced parallel exhaust from the core plasma into the scrape-off-layer and to the divertor targets. Further, regions of stochasticity inside the separatrix can lead to enhanced perpendicular transport, even if these field lines do not themselves escape to the wall. Based on magneto-hydrodynamic (MHD) modeling, it has been previously proposed that a particular resonant response to the applied RMP fields--the so called "Edge-Peeling" response--enhances these geometric changes and thus drives enhanced exhaust. How much these mechanisms contribute to the overall pump-out is an open question. Further, how these RMPs impact the fundamental coupling between the plasma core, edge, and scrape-off-layer, through changes to particle fueling and particle exhaust, is the subject of this thesis. The EMC3-EIRENE code is utilized to assess these scenarios on the Mega-Ampere Spherical Tokamak (MAST) and it's upgrade (MAST-U). Initially, work was carried out to validate the theoretical mechanism for enhanced exhaust: that pressure gradients drive flows along open field lines in the plasma edge. Modeling showed that flows generated by local gas puffing are robust to changes in plasma parameters, and ultimately are a fundamental feature that can be experimentally validated. The underlying mechanism of static pressure driven flows was resolved with a 1D model. Modeling was then used to study the impact of RMP fields specifically. The inclusion of plasma response (from a resistive single fluid MHD model) in the RMP fields shows a more moderate response of density and temperature to the RMPs than does a vacuum field approach in MAST lower single null discharges. In this scenario, enhanced exhaust is shown to contribute to the density pump-out, but the modeled confinement changes underpredict the impact expected from analysis of experiments. Applying this same approach in MAST double null discharges--a second test case from experiment--shows that the addition of RMPs with the single fluid Edge-Peeling response does not cause a consistent pump-out signature in the modeling. This numerical finding of no density pump-out is in contrast to experimental observations for such configurations. This is found in spite of the fact that field lines are escaping the confined region, pressure driven flows are formed, and characteristic lobe structures appear in the plasma edge. This study has shown in a consistent manner that pressure driven flows along field lines are a viable mechanism to govern the plasma particle exhaust from the edge reservoir. If 3D magnetic flux bundles generated by RMP fields connect to regions deep inside of the separatrix, the parallel pressure gradient towards divertor targets will drive enhanced particle flux out of the formerly confined region of the plasma. If the length scale of connection is too long such that the parallel pressure gradient can not be maintained, the flow vanishes, and in spite of the nominal 3D structures in the magnetic field, no impact on particle exhaust is seen. This finding is important for the efforts to understand plasma exhaust with RMP fields. The mere existence of the 3D lobes of the separatrix, formed by the RMP fields, is not sufficient to explain the plasma density pump out alone. But for plasma scenarios with short connection length, and magnetic fields characterized by steep radial gradients they are a viable contributor.