We examine the influence of surface charge on the percolation, gel-point and phase behavior of cellulose nanocrystal (CNC) suspensions in relation to their nonlinear rheological material response. Desulfation decreases CNC surface charge density which leads to an increase in attractive forces between CNCs. Therefore, by considering sulfated and desulfated CNC suspensions, we are comparing CNC systems that differ in their percolation and gel-point concentrations relative to their phase transition concentrations. The results show that independently of whether the gel-point (linear viscoelasticity, LVE) occurs at the biphasic - liquid crystalline transition (sulfated CNC) or at the isotropic - quasi-biphasic transition (desulfated CNC), the nonlinear behavior appears to mark the existence of a weakly percolated network at lower concentrations. Above this percolation threshold, nonlinear material parameters are sensitive to the phase and gelation behavior as determined in static (phase) and LVE conditions (gel-point). However, the change in material response in nonlinear conditions can occur at higher concentrations than identified through polarized optical microscopy, suggesting that the nonlinear deformations could distort the suspensions microstructure such that for example a liquid crystalline phase (static) suspension could show microstructural dynamics similar to a biphasic system.