Is it common for one to have bad breath while sleep deprived?

Yes If Dehydrated: When you are sleep deprived, you throw your whole system off. If you are not eating properly & not taking in enough water, the bacteria in the mouth will have a field day and produce bad breath.

Help deprived: Is it possible that while you were being sleep deprived you also ignored some of your daily routines, especially your home oral care. If you did that may e the connection. Concentrate on your home care and see a dentist for a checkup to rule out other dental causes.