In a more complicated answer: maybe.
Polariser affects light reflections of all sorts of objects not just water and the sky. Typically it can reduce the shine on organic objects quite well which is why green grass gets such a boost when the polariser is correctly positioned. That said it can also eliminate the shine of natural skin oils, making the person look like they are made from diffuse fabric. Not a good look by any means in my opinion. That said. It's art. Try it have a look if you like it then good for you.
CPL is great for nice deep blue skies (no help on overcast day though). Also they are good for controlling / allowing reflections in glass and reflective metals / materials. An example of this would be trying to shoot through a glass window at a store display, maybe seeing through the car window vs. reflection of surroundings.
These guys pretty much have it. In general, I'd recommend not using a polarizer for portraits, unless you actively decide that you need to reduce glare, or heighten the colors a bit. There is no single "always correct" answer, as with most things.