In the Black Book of the Admiralty (with its laws likely dating from around the late 13th early 14th century) sleeping whilst on watch was punishable in four stages, the first two a bucket of cold water, the third tying to the mast with weights on the arms and likely a flogging, the fourth would see a man hung in a basket from the bowsprit with a loaf of bread and a knife, giving him the choice between starvation, or a slow death adrift if he decided to cut himself loose.

By the time of the Napoleonic Wars the 1757 Articles of War were in place, which noted in article 26

"No person in or belonging to the fleet shall sleep upon his watch, or negligently perform the duty imposed on him, or forsake his station, upon pain of death, or such other punishment as a court martial shall think fit to impose, and as the circumstances of the case shall require."

Making death by no means a certainty, but likely a reality if it were to happen the four times required in the Black Book. Which considering that the offense essentially places the entire crew in danger is unsurprising.