I don't think that any of these panel lights could harm a sensor.
A flat field makes it easier to see what we are looking for, and can make sure that the whole frame is filled with a blanket of light. There are other ways, of course, like shining the lamp on a wall and photographing that, but that makes it harder to use fast shutter speeds without also getting a lot of noise or "under-exposing" and it might get easy to confuse sensor banding noise with light-source banding. One alternative is to put a smooth diffusing material in front of the lamp to get rid of any visibility of individual LEDs.
A bright (but not clipped) flat field, the fastest shutter speed, and the slowest rolling shutter will be the easiest context to see banding in. If you see none there, then you won't see any with a slower shutter speed, or a faster rolling shutter. If you do see it at the fastest shutter speed, then you can try various slower speeds and see where the practical limit is for that light panel. Of course, you don't want to try this will full panel intensity, as that could easily mean no strobing, even in a panel that does strobe at lower intensities. Keep in mind that if you choose one relatively low shutter speed and check for banding, and you don't see any, it may be just a lucky choice that is an exact integer multiple of the light cycle, and 1/3 stop slower or faster could reveal banding.
The 1MHz cycles that Bob speaks of would not cause visible banding, even at 1/16000. At 40KHz, like Jim was talking about, a panel without phosphors and partial intensity could show shallow banding at 1/16000, but he says the phosphors smooth things out, so that might not be an issue. Most panels are typically used for much slower shutter speeds, though, where you wouldn't expect a visible problem.