We investigate the nonequilibrium relaxation dynamics of the one-dimensional (1D) Fermi-Hubbard model subjected to abrupt, global interaction quenches. Specifically, we benchmark the convergence properties, structural accuracy, and algorithmic breakdown of the Magnus expansion against numerically exact results obtained via full Exact Diagonalization (ED) on small, periodic lattice clusters. By tracking the real-time evolution of local observables, double occupancy (doublon density), and many-body state fidelity metrics, we map out the validity bounds of the low-order Magnus series across weak, moderate, and strong interaction regimes. Our findings demonstrate that while the Magnus expansion provides an exceptionally accurate description of short-time coherent dynamics, rapid phase matching, and initial prethermalization tendencies, its convergence is fundamentally bottlenecked at longer timescales. This breakdown is driven by the rapid growth of multi-particle entanglement, non-local operator spreading via nested commutators, and the emergence of severe state-space fragmentation inherent to dense, strongly interacting many-body spectra.