You will never visually see flicker on an LCD unless it's malfunctioning or you have activated black frame insertion. But the flicker is still there on PWM equiped ones, only visible with special equipment or slow motion cameras.
The problem them is that your brain might be subconsciously sensitive to some specific flicker patterns, resulting in the aforementioned headaches.
And I definitely notice the flicker in a CRT, especially when I'm not looking straight at it (oddly). Heck, I see the flicker of LED Christmas lights.