No, they don't, unless there's something wrong with the shutter. They may appear to be a full white frame, but at 1/1000th the shutter is a fairly narrow slit. Using a flash on single burst will verify this.
It will be with any focal plane shutter above maximum sync. speed.Except my Pentax Spotmatic which also does not work at 1/500th and 1/1000th. It has a horizontal cloth shutter though, but the effect is the same.

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