We report on the experimental characterization of the effect that a passive plasma lens in the overdense regime has on high-brightness bunch quality by means of 6D phase-space analysis. The passive lens is generated by confining hydrogen gas with a capillary tube pre-ionized with a high-voltage discharge. We observed that the optimum condition is retrieved at the end of the overdense regime with almost no effect on bunch brightness. The presence of gas jets, leaking from the hollow capillary end-points, extends the lens effects also outside of the capillary, resulting in longer focusing channels. Experimental results are supported with numerical simulations of the complete accelerator line together with the plasma channel section.