If the opportunity to sleep arises while on call often this is a proposition that is easier said than done. Sleep too soundly and risk not hearing the pager go off, or what may be even worse, be a half awake, confused, babbling idiot when talking to the ER doc about an admission. Certainly I have heard tales of doctors not remembering who they talked to the next morning and I have heard of more than one doctor falling asleep again while on the phone.
Because of this I tend to be one who sleeps with one eye open while on call. Some of my worse nights of sleep can be when the pager is totally silent. I look at it on my night stand just taunting me saying, "You don't know when I'm going to go off, ha-ha."
There's no way to win while on call. Call is call.