Friction drag at the surface in atmospheric boundary layers (ABLs) is the most challenging flux quantity to infer from observations and simulations of mean wind speed profiles and requires an appeal to similarity theories. Recently, we have reported a new scaling framework and predictive model for drag in non-convective, smooth-walled laboratory turbulent boundary layers (lab TBLs) (Dixit et al. in Phys Fluids 32(4) [1]). Here, we evaluate this predictive model for a specific class of ABLs called truly neutral ABLs (TNABLs) through large-eddy simulations (LES). TNABL is free from convection effects at its upper as well as lower boundaries and therefore bears the closest correspondence to lab TBLs in that respect. From the viewpoint of testing scaling laws, TNABLs present attractive friction Reynolds numbers two to three orders of magnitude higher than the largest Reynolds numbers achieved in lab TBLs to date. The LES study reported here uses the weather and research forecasting (WRF) model in ideal simulation mode. Specifically, we attempt to understand the role of surface roughness in the LES of TNABLs toward the applicability of our predictive drag model. Our results show that the drag scaling and predictive model show promising potential to handle TNABLs provided that the roughness length typical of laboratory experiments is set for WRF simulations.