Yes, in English too 'the boss sleeps at work' suggests that he spends so much time at the office that he ends up sleeping there instead of at home; to say that 'the boss sleeps on the job' definitely means that he is asleep when he should be working. So the only correct translation for this Danish should be 'the boss sleeps at work' - right?
"Sleeps on the job" and "sleeps at work" are both accepted as correct, but they mean rather different things. The first means he sleeps when he should be working, the second that (perhaps because he works so late) he doesn't go home to sleep, but sleeps at the workplace instead. Which meaning is nearer to what the Danish actually means?