Clustering of dark matter halos has been shown to depend on halo properties beyond mass such as halo concentration, a phenomenon referred to as halo assembly bias. Standard halo occupation modeling (HOD) in large scale structure studies assumes that halo mass alone is sufficient in characterizing the connection between galaxies and halos. Modeling of galaxy clustering can face systematic effects if the number of galaxies are correlated with other halo properties. Using the Small MultiDark-Planck high resolution $N$-body simulation and the measurements of the projected two-point correlation function and the number density of Sloan Digital Sky Survey (SDSS) DR7 main galaxy sample, we investigate the extent to which the dependence of halo occupation on halo concentration can be constrained, and to what extent allowing for this dependence can improve our modeling of galaxy clustering. Given the SDSS clustering data, our constraints on HOD with assembly bias, suggests that satellite population is not correlated with halo concentration at fixed halo mass. Furthermore, in terms of the occupation of centrals at fixed halo mass, our results favor lack of correlation with halo concentration in the most luminous samples ($M_{\rm r}