For me, personally, when sleeping with or without diapers, the amount of sleep I get is about the same. For the quality of my rest, I find putting on diapers as a temporary solution to keep my mind off about not wetting the bed.
During the night, if my brain clicks, I'd usually check on my diaper if I think I may have overfilled it, but most of the time, I would sleep through the night remembering nothing. Waking up can be the most enjoyable time, or the most uncomfortable time depending on the situation of my diaper. If I'd wet the diaper earlier in the night, my diaper would be cold, if I'd wet the diaper closer to the morning, it would stay relatively warm. Waking up to a cold diaper at times is very unsettling because the texture of the soiled parts tend to become sticky or moist.
On a normal day, I would usually rewet the diaper while brushing so that the chances for a diaper leak is kept at a minimal and that the diaper is used up. I would take a shower before going off to school. During weekends, I would often get up, make myself a coffee, tea or hot water, then head back to my bed and enjoy the morning in my wet diaper. I would change after I've finished enjoying my hot beverage or after I managed to rewet the diaper.