Depends on the age of the baby. For a newborn to 1 year old I would change the diaper at night as for awhile you'll be up at night doing middle of the night feedings anyway.
Once your baby get's past 1 year old they usually start sleeping through the night and then as long as the baby is asleep I wouldn't wake the baby to change the wet diaper.
Just make sure you apply powder and diaper rash cream to protect against diaper rash and the baby should be fine sleeping in a wet diaper.