An article at MSNBC talks about the controversy of pilots sleeping while in flight.  The discussion about airline pilots is a separate issue; the article specifically mentions military pilots, however:

Even a 10-minute nap can improve a pilot’s performance, said Scott Shappell, a Clemson University professor who as director of the Human Factors Institute helped write the flying policies that govern military pilots.

In the military, pilots flying alone have been allowed for decades to take naps, Shappell said. “I can tell you absolutely, but good luck trying to find proof of this, in the military we have single-seat pilots take naps,” he said. Read more