I think that the meaning is different for "addormentarsi sugli allori": to rest on one's laurels, if I am not mistaken. "Asleep at the switch/ wheel" has more of the meaning of not doing one's job or letting someone down in its idiomatic sense.
Sorry, I forgot to water your plants and they all died. I must have been asleep at the switch!
Wow, he won 3 gold medals in the Olympics! Now I guess he can rest on his laurels.
No, no, no... "addormentarsi sugli allori" means that you might lose a game just because you think you are so much the best that you end up playing bad... (Si sono addormentati sugli allori... e hanno perso miseramente la partita. Che gli serva di lezione!)
"addormentarsi sugli allori" is a bad thing. In Italian, you cannot use it in the 3-gold-medals example. It'd be weird.
However, it cannot be used in the water-your-plants example either because that example does not involve any "allori"... So, I guess, it can translate "fall asleep at the switch" only in a victory/game/quick-response context.
Definition from the FreeDictionary: fall asleep at the switch
be asleep at the switch - if someone is asleep at the switch, they are not ready to act quickly to avoid problems and do their job well. The Party was simply too confident of victory and fell asleep at the switch.
Random peice of news just found onthe web: Millions Drive Drowsy and Fall Asleep at the Wheel National Sleep Foundation Issues Wake-Up Call to Fatigued Drivers - Stop and Nap or Drink Caffeine!