In both cases they are (or at least can be) wholly unconscious when sleeping. This can be seen from two of the stories in the Pārājika section of the Vinaya, in which two arahant bhikkhus were so deeply asleep that they failed to wake up even when some passing women stopped to have sex with them.
At one time a monk was lying down in the Jātiyā Grove at Bhaddiya, having gone there to spend the day, and he had an erection because of wind. A certain woman saw him and sat down on his penis, and having taken her pleasure, she departed. The monks, seeing the moisture, informed the Master. “Monks, an erection occurs for five reasons: because of sensual desire, because of excrement, because of urine, because of wind, because of being stung by caterpillars. It’s impossible that that monk had an erection because of sensual desire. That monk is a perfected one [arahant]. There’s no offence for that monk.”
At one time a monk had gone to spend the day in the hall with the peaked roof in the Great Wood near Vesālī. He opened the door and lay down, and he had an erection because of wind. Just then a number of women, bringing scents and garlands, came to the monastery to look at the monastic dwellings. Those women saw that monk and they sat down on his penis. Having taken their pleasure, they said, “What a bull of a man,” and they put up their scents and garlands and departed. The monks saw the moisture and informed the Master.
“Monks, an erection occurs for five reasons: because of sensual desire, because of excrement, because of urine, because of wind, because of being stung by caterpillars. It’s impossible that that monk had an erection because of sensual desire. That monk is a perfected one. There’s no offense for that monk. But, monks, you should close the door when you are in seclusion during the day.”