This paper is the continuation of a technical paper which is called "Detailed Electromagnetic Design of an Integrated and Compact 1.3 GHz Superconducting Radio Frequency (SRF) Electron Source" [1]. In the previous paper, we examined if a promising RF electromagnetic design of the gun and cathode region could be achieved. Further, we examined if this gun region could be fully integrated, in terms of the electromagnetic RF design, with the rest of the accelerator, keeping in mind the overall goal of compactness and reduction of duplicative infrastructure commonly associated with separated function electron guns and structures. While we convinced ourselves thus far that the RF electromagnetic design of our concept is feasible, we also needed to perform particle tracking to assess the beam properties through the entire system, understand and remediate any beam loss. For this step, we examined the cathode region and analyzed the gating process of the thermionic cathode, as losses would most likely be attributed to releasing electrons into the accelerating structure during an unfavorable phase window.