Density functional theory calculations are performed to study the influence of Na adatoms on the electron transport and structural properties of the In-Si(111)($4\ifmmode\times\else×\fi{}1$)\char21{}($8\ifmmode\times\else×\fi{}2$) nanowire array. It is found that there are several energetically nearly degenerate Na adsorption sites, the precise energetic ordering of which depends on the surface coverage. Irrespective of the adsorption site, the adatoms show mainly a repulsive interaction with little indications for long-range correlation. The calculations show only a moderate disturbance of the quantum conductance of the metallic room-temperature ($4\ifmmode\times\else×\fi{}1$) In nanowire phase upon Na adsorption. Also, the electronic density of states at the Fermi energy is only slightly modified. However, it is found that adsorption-induced strain as well as charge donation into the In nanowires lead to a noticeable decrease of the metal-insulator transition temperature. Therefore, Na adsorption on the semiconducting ($8\ifmmode\times\else×\fi{}2$) In nanowire phase may trigger a transition into the metallic state.