Harmonic balance (HB) or time-spectral (TS) methods are commonly used as an alternative to conventional implicit approaches to reduce the computational cost in time-periodic flows, such as turbomachinery analyses. HB/TS approaches are based on a system of coupled equations for all the time instants. This coupling results in significant modifications in the code structure to implement the HB/TS approach in conventional implicit CFD solvers. Alternatively, the pseudo-spectral time marching (PSpTM) method proposes a decoupled time-marching definition of the spectral time derivative, requiring minor changes in the CFD solver structure. In this work, the PSpTM method is applied for the first time to evaluate a fan stage's aerodynamic and aeromechanic responses under complex upstream distortion. The PSpTM method was implemented into an existing unstructured edge-based, second-order, compressible RANS solver. The well-established implicit second-order backward difference (BDF2) scheme is used as a benchmark. A 60-deg sector distortion screen was used to define the upstream perturbation of an isolated fan rotor. Based on the different requirements of aerodynamic and aeroelastic fan analyses, quasi-3D and 3D rotor models were used to determine the accuracy and computational cost reduction achieved with the PSpTM model. For aerodynamic analyses, a speed-up factor of up to 8 was obtained concerning the BDF2 method. Depending on the accuracy required, speed-up factors of around 2-6 can be achieved for unsteady aeroelastic and aeroacoustic analyses.