Wide angle lens & polarizer

I know that when using a polarizer on a wide angle lens, blue skies aren't evenly polarized. If the skies are cloudy will the polarizer have any uneven effects on the sky?

Thanks.

Polarizers only have effect on polarized light. To generate polarized light, you need unidirectional light (sun) to reflect off the atmosferic haze. Cloudy skies won't "emmit" polarized light by themselves, so the polarizer would have no effect at all. Sill, you'd be able to get polarized light at ground level even under cloudy skies, if the light coming from the sky is reflected by a reflective surface like windows etc.

Thanks for the answer!

Polarizers have the side effect of increasing contrast though, so the blue parts of the sky go a darker shade of blue and the white parts stay white.