if you use a compliant flash attaching via the TTL pins, the camera will not allow you to increase shutter faster than the x-sync for that flash-camera combination!
thus can use a Canon flash directly, but if using an Olympus flash, must use a simple one-pin hotshoe adapter so the camera does not detect it is a compliant flash unit
of course, the flash cannot use TTL exposure, and you must resort to Auto or, preferably, just Manual flash exposure
with the OM-D's, a shutter of 1/400th sec will result in a small area at the TOP of the image not being lit by flash - this is fine if you have no subject there, at 1/500th sec, you have almost half the top not being lit by flash - this may still be manageable depending upon your subject
if you have a camera such as the Panasonic LX-100 which has a shutter inside the lens, it will sync all the way up to 1/4000th sec with full flash output and with full frame coverage (not Super FP or HSS mode which is useless for key shifting)