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The LCD monitor is blacked out during H* shooting. If you put the camera in LiveView mode before shooting, you can see the scene on the rear LCD monitor before and after the H* shooting cycle, but not during. There is no appreciable time lag when pushing the shutter button to start the shooting cycle, but there is about a 2 sec lag after it ends, before the LV display is up again.
Page 113 and 330 of the manual describe limitations on max speed associated with shutter speed, ISO and image recording settings.
On pg 113, the manual says that when you set H* mode, the <H> will blink on the top LCD panel and the H* icon will be displayed on the LCD monitor. On my 1DX, I see the blinky H, but nothing on the LCD monitor. My firmware and manual are up to date.