For an emergency descent you would expect the pilot to select 10000ft in the window, or MSA if higher before initiating descent. Although some airlines train spinning something lower, getting it going down and then refining it. It would be unusual to set something below 10000ft. The cabin crew would only check on the flight crew if the aircraft didn't descend after a decompression.
But obviously the first action is to always don the oxygen mask and it would be strange not to.