Yes, it is possible.
In Arizona there are numerous ways one can be convicted of DUI. One way you can be convicted is for being in actual physical control of a vehicle while under the influence of alcohol. The issue of being in acual physical control is for a jury to decide, and they will take into account a number of factors: Were you sleeping? Was the engine on? Was the vehicle in gear? Was the brake on? Were your windows up or down? Was the radio on? Where was the vehicle located? How was the weather? Were the keys in the ignition? Was the public in danger?
It is important to have an experienced DUI lawyer look over your case if you were arrested for DUI while you were sleeping in your vehicle.