Boundary Layer Ingestion (BLI) appears to be a promising solution to meet aggressive aviation fuel burn and environmental goals defined by NASA and other entities. Propulsion-airframe integration plays a critical role in BLI vehicle design given the strong coupling between the airframe and the propulsion system. Several studies have focused on flow field impacts on the propulsion system performance, but have ignored the effect of the propulsor on the flow field. Recent studies, however, have focused on both aspects, highlighting the need for capturing this interdisciplinary coupling. Multidisciplinary analyses (MDA), especially those involving CFD, are computationally expensive and are not suitable in the conceptual design of BLI propulsion systems. This paper aims to provide a less expensive approach by developing a parametric formulation for the effect of the propulsion system on the flow field, which can then be used in BLI propulsor conceptual design. This paper quantifies the sensitivity of the changes in the flow field due to the on-design and off-design parameters of the propulsion system. In addition, it also illustrates the difference in propulsion system design and performance when the throttle dependent effects on the flow field is captured, to the case where it is not. Distortion impacts on engine sizing and performance are also considered in this paper.