Spiral plate heat exchangers (SHE) have been proven in industrial applications involving viscous and fouling fluids. Their simplified maintenance requirements and high heat transfer capacity make them a great candidate for Molten Salt Reactor (MSR) applications. While traditional tube-and-shell heat exchangers also have proven industrial success, their complexity and significant maintenance requirements are disadvantageous in the corrosive environment of MSRs. Because the fuel salt of liquid fueled MSRs often passes through an external heat exchanger in a compact geometry with a potentially moderating secondary fluid, it is important to understand which conditions might lead to a criticality accident. Monte Carlo N-Particle® (MCNP®) code allows simulation of the criticality of the system and the neutron flux across the system. We evaluate the system's multiplication factor for several geometries and materials through parametric studies by varying SHE sizes, hot/cold channel gaps, and plate thickness for selected structural materials, fuel salts, and secondary loop heat transfer fluids. We characterize which configurations will likely lead to a critical system and identify some of the important SHE design considerations from a criticality perspective. Additionally, this work suggests the possibility of novel spiral MSR reactor core designs with an integrated heat exchanger under specific conditions.