In this letter, we investigate how network densification influences the performance of downlink cellular network in terms of coverage probability (CP) and area spectral efficiency (ASE). To model the decay of signal power caused by pathloss, we apply a realistic bounded pathloss model. It is shown that network densification indeed degrades CP when the base station (BS) density lambda is sufficiently large. Moreover, we shed light on the impact of ultra-dense deployment of BSs on the ASE scaling law. Specifically, it is proved that cellular network ASE scales with rate lambda e(=kappa lambda), i.e., first increases with lambda and then diminishes to zero as lambda goes to infinity.