A CP filter cuts light reflected by non-metalic surfaces. It achieves this by blocking all light a little, and polarized light a lot. You can rotate the filter to align it, and the effect increases with proper alignment, so you can rotate the filter to have almost no effect, through having a strong effect. It is useful for seeing through windows, or into water, and for making leaves and sky more saturated.
As you swing off the axis of sunlight, the effect will increase until you are perpendicular to the axis. I haven’t considered it, or paid enough attention when using it, but if the sun were right overhead, and you are shooting horizontally, presumably north, south, east or west would all be perpendicular to the sun, so it should work pretty well. I use lens hoods most of the time, they interfere with turning the filter, so I only use the filter when I really need to, and not so much for deeper blue sky.
Consider this scene near the Capilano Suspension Bridge, in North Vancouver, taken without a filter
… and the same scene again with a CP filter adjusted to reduce reflection, 4 seconds earlier
I don’t think I have any before and after of the sky, but I hope this helps highlight how the CP filter can help.