Hi again, the question made me curious so I made a not too scientific test with only my basic Hoya CPL on the 10-22. (According to a ruler in my drawer this CPL is about 8 mm thick.)

At 10 mm the CPL is still slightly visible in the far corners. At 11 mm it's no longer visible, but it adds some vignetting compared to shooting with the bare lens. At 12 mm and above I see no significant difference between lens with/without CPL with respect to vignetting. So, if you want to shoot at 10 mm with a CPL it should be thinner than 8 mm. Hope this answers your questions.