We present light-cone-integrated simulations of the cosmic microwave background (CMB) polarization signal induced by a single scattering in the direction of clusters of galaxies and filaments. We characterize the statistical properties of the induced polarization signals from the presence of the CMB quadrupole component (pqiCMB) and as the result of the transverse motion of ionized gas clouds with respect to the CMB rest frame (pβ2 t SZ). From adiabatic N-body/hydrodynamic simulations, we generated 28 random sky patches integrated along the light cone, each with about 0.86 deg2 and angular resolution of 6''. Our simulation method involves a box-stacking scheme that allows to reconstruct the CMB quadrupole component and the gas physical properties along the line of sight. We find that the linear polarization degree in the logarithmic scale of both effects follows approximately a Gaussian distribution and the mean total signal is about 10–8 and 10–10 for the pqiCMB and pβ2 t SZ effects, respectively. The polarization angle is consistent with a flat distribution in both cases. From the mean distributions of the polarization degree with redshift, the highest peak is found at z sime 1 for the induced CMB quadrupole and at z sime 0.5 for the kinematic component. Our results suggest that most of the contribution for the total polarization signal arises from z lesssim 4 for the pqiCMB and z lesssim 3 for pβ2 t SZ. The spectral dependency of both integrated signals is strong, increasing with the frequency, especially in the case of the pβ2 t SZ signal, which increases by a factor of 100 from 30 GHz to 675 GHz. The maxima values found at the highest frequency are about 3 μK and 13 μK for the pqiCMB and pβ2 t SZ, respectively. The angular power spectra of these effects peak at large multipoles ℓ > 104, being of the order of 10–5 μK2 for pqiCMB polarization and 10–7 μK2 for the pβ2 t SZ effect. Therefore, these effects will not be a relevant source of contamination for measurements of the primary polarization modes, and at larger multipoles of roughly ℓ > 40, 000, pqiCMB may be the dominant component over the primary and lensing signals.