The filters I use (dichroics) have different efficiencies depending on the polarization of the incident light (s- or p- polarization), so I expect they can indeed polarize the incident light somewhat. The polarizing efficiency of the dichroic filter is much lower than a polarizer, tho.
It's possible to design filters to have very high pass efficiencies for both the s- and p- states, so they would not induce any large amount of polarization.