Total cavopulmonary connection is the result of a series of palliative surgical repairs performed on patients with single ventricle heart defects. The resulting anatomy has complex and unsteady hemodynamics characterized by flow mixing and flow separation. Although varying degrees of flow pulsatility have been observed in vivo, non-pulsatile (time-averaged) boundary conditions have traditionally been assumed in hemodynamic modeling, and only recently have pulsatile conditions been incorporated without completely characterizing their effect or importance. In this study, 3D numerical simulations with both pulsatile and non-pulsatile boundary conditions were performed for 24 patients with different anatomies and flow boundary conditions from Georgia Tech database. Flow structures, energy dissipation rates and pressure drops were compared under rest and simulated exercise conditions. It was found that flow pulsatility is the primary factor in determining the appropriate choice of boundary conditions, whereas the anatomic configuration and cardiac output had secondary effects. Results show that the hemodynamics can be strongly influenced by the presence of pulsatile flow. However, there was a minimum pulsatility threshold, identified by defining a weighted pulsatility index (wPI), above which the influence was significant. It was shown that when wPI < 30%, the relative error in hemodynamic predictions using time-averaged boundary conditions was less than 10% compared to pulsatile simulations. In addition, when wPI < 50, the relative error was less than 20%. A correlation was introduced to relate wPI to the relative error in predicting the flow metrics with non-pulsatile flow conditions.