Unfortunately, due to many different factors, this is not only improbable, but also impossible, as climbers barely carry enough supplies to make the trip, the extremely irregular terrain, and the sled would have so much speed almost immediately that you wouldn't be able to go around hazards or even stop.
Though doing that would be really funny, and if you try to do that, you would officially be "Built different" than all of those non-mount Everest sledders(as long as you survive, of course).
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