Quantitative studies of capillarity-driven pinching and extensional rheology of aqueous solutions of polysaccharides like hydroxyethyl cellulose (HEC) are beyond the measurable range of most extensional rheometers, and are relatively rare, even though polysaccharides are widely used as rheology modifiers. In this study, we utilize dripping-onto-substrate (DoS) rheometry protocols that we recently developed to characterize the pinching dynamics and extensional rheology response of aqueous HEC solutions. We find that the radius evolution data from the pinching necks show an elastocapillary regime that can be fit to determine the extensional relaxation time even for unentangled HEC solutions that show neither rate-dependent regime in shear viscosity nor measurable elasticity in the shear rheology response measured using torsional rheometers. Furthermore, the radius evolution data for the entangled HEC solutions display a power law regime, previously reported only for multicomponent complex fluids containing particles, bubbles, drops, and lamellar gel networks described with the generalized Newtonian fluid models. However, the entangled HEC solutions that exhibit pronounced shear thinning and measurable elastic moduli also reveal that the power law in the radius evolution data is modulated in the late stage by viscoelastic effects, allowing the measurement of both extensional relaxation time and steady, terminal extensional viscosity. Finally, we show that the pinching dynamics underlying drop formation/liquid transfer of HEC solutions can be determined fairly accurately by measuring shear rheology response, unlike the solutions of flexible polymers that display a stark contrast in response to shear and extensional flows.