Monte Carlo sampling is frequently employed for uncertainty quantification in depletion calculations. Several assumptions are needed to perform this analysis. In this work, an assessment of these assumptions is proposed via sample convergence studies and perturbation of the sampling distribution. The Uncertainty Analysis in Best-Estimate Modeling (UAM) Pincell Hot Full Power and the Turkey Point reference cases were considered for this purpose. The 235U thermal independent fission yield uncertainties evaluated in JEFF-3.3 and JEFF-4.0 were propagated to the nuclide vector and to the system multiplication factor. Using JEFF-4.0 data, a 75% reduction in the uncertainty of selected nuclide concentrations and an 80% reduction in the multiplication factor uncertainty were observed, showcasing the effect of full covariance evaluations. The presented results also prove that the uncertainty in the considered observables shows marginal dependence on the sampling distribution.