The dynamics of Na atoms on the surface of helium nanodroplets following excitation via the 3p <- 3s transition has been investigated using state-specific ion-based detection of the products. Excitation of the system to the 3p (2)Pi states is found to lead to the desorption of both bare Na and NaHe exciplexes. The associated speed distributions point to an impulsive desorption process for Na products and a thermally driven process for the NaHe exciplexes. In contrast, excitation of the 3p (2)Sigma state leads exclusively to the impulsive desorption of Na atoms. In this case, the desorption is accompanied by a helium-induced relaxation process, as evidenced by the large fraction of detected Na P-2(1/2) atoms. The relaxation process is thought to be related to a crossing between the 2 Pi(1/2) and (2)Sigma potential energy curves at large distance.