In species with large population sizes such as Drosophila, natural selection may have substantial effects on genetic diversity and divergence. However, the implications of this widespread nonneutrality for standard population genetic assumptions and practices remain poorly resolved. Here, we assess the consequences of recurrent hitchhiking (RHH), in which selective sweeps occur at a given rate randomly across the genome. We use forward simulations to examine two published RHH models for D. melanogaster, reflecting relatively common/weak and rare/strong selection. We find that unlike the rare/strong RHH model, the common/weak model entails a slight degree of Hill-Robertson interference in high recombination regions. We also find that the common/weak RHH model is more consistent with our genome-wide estimate of the proportion of substitutions fixed by natural selection between D. melanogaster and D. simulans (19%). Finally, we examine how these models of RHH might bias demographic inference. We find that these RHH scenarios can bias demographic parameter estimation, but such biases are weaker for parameters relating recently diverged populations, and for the common/weak RHH model in general. Thus, even for species with important genome-wide impacts of selective sweeps, neutralist demographic inference can have some utility in understanding the histories of recently diverged populations.