Hopefully you're not going to get a reflection off your subject, so not sure why you'd use a CPL, other than as a makeshift ND filter in order to use a wide aperture in bright light for DoF reasons.
No issue, apart from if you want to use studio flashes, or 3rd party flashes without HSS, when you can't go above the sync speed, so you might need ND filters then.
Thanks
How about for reflections from glasses?
That's an interesting question - never thought of it before and no idea about the answer, but assume that yes, it will reduce reflections - not hot-spots though..
Hot-spots?