Pressurized solid oxide fuel cell (SOFC) systems are a sustainable opportunity for improvement over conventional systems, featuring high electric efficiency, potential for cogeneration applications, and low carbon emissions. Such systems are usually analyzed in deterministic conditions. However, it is widely demonstrated that such systems are affected significantly by uncertainties, both in component performance and operating parameters. This paper aims to study the propagation of uncertainties related both to the fuel cell (ohmic losses, anode ejector diameter, and fuel gas composition) and the gas turbine cycle characteristics (compressor and turbine efficiencies, recuperator pressure losses). The analysis is carried out on an innovative hybrid system layout, where a turbocharger is used to pressurize the fuel cell, promising better cost effectiveness then a microturbine-based hybrid system, at small scales. Due to plant complexity and high computational effort required by uncertainty quantification methodologies, a response surface (RS) is created. To evaluate the impact of the aforementioned uncertainties on the relevant system outputs, such as overall efficiency and net electrical power, the Monte Carlo method is applied to the RS. Particular attention is focused on the impact of uncertainties on the opening of the turbocharger wastegate valve, which is aimed at satisfying the fuel cell constraints at each operating condition.