The streaming instability has been identified as a promising mechanism to concentrate solids and promote planetesimal formation in the midplane of disks. It has been demonstrated in Squire & Hopkins (2018) that a related settling (and streaming) instability (here SSI) occurs as particles sediment towards the midplane. However, the ability of the SSI to concentrate solids and generate turbulence is yet to be addressed. To shed light on this aspect, we present a systematic study of the saturated state of the SSI by performing a series of numerical simulations with the multi-fluid version of the FARGO3D code. We furthermore have extended the existing linear analysis to more realistic scenarios including particle size distributions and background disk turbulence. Our findings suggest that particle clumping is too weak to trigger planetesimal formation during the settling of particles, but the SSI could generate weak levels of turbulence in otherwise nearly laminar regimes.