Non-equilibrium inductively coupled plasmas (ICPs) operating in hydrogen are of significant interest for applications including large-area materials processing. The spatial distribution of the atomic hydrogen is of significant importance. Increasing control of spatial gas heating, which drives the formation of neutral species density gradients and the rate of gas-temperature-dependent reactions, is critical. In this study, we use 2D fluid-kinetic simulations with the Hybrid Plasma Equipment Model to investigate the spatially resolved production of atomic hydrogen in a low-pressure planar ICP operating in pure hydrogen (10 - 20 Pa or 0.075 - 0.15 Torr, 300 W). The reaction set incorporates self-consistent calculation of the spatially resolved gas temperature and 14 vibrationally excited states. We find that the formation of neutral-gas density gradients, which result from spatially non-uniform electrical power deposition at constant pressure, can drive significant variations in the vibrational distribution function and density of atomic hydrogen when gas heating is spatially resolved. This highlights the significance of spatial gas heating on the production of reactive species in relatively high-power-density plasma processing sources.