Probably not.
It wouldn't do anything to darken the sky, a polarizer only does that during the daytime because it suppresses reflected polarized light -- light reflected from the sun by water molecules in the air. At night when there's no sun, the polarizer won't darken the sky.
It might possibly be useful to suppress reflections from some windows, etc. -- but often you *want* those reflections in a night time cityscape.
So -- no.