I never thought as sleep as an addiction.
I am not sure where you are in your recovery, but sleep is pretty important in the process. At first, you are usually pretty exhausted. (staying up drinking instead of sleeping, never hitting the right levels of REM to feel properly rested, physical withdrawal will lead to exhaustion) Then there is living life and experiencing feelings we are not used to. These feelings can definately overwhelm us and cause us to be sleepy.
This sleepiness can hang on for quite awhile (it did in my case).
I hope that VETERAN AAers help me with this one...but their is a saying at the meetings about the acronym HALT. As you are in recovery, these are things to keep in mind about what is going on with you and to take care of during the process.
Hungry...eat when you are.
Angry...find solutions to it (call sponsor, use phone tree, walk, etc.)
Lonely...find solutions to it (call sponsor, use phone tree, walk where there are people like in a park or downtown shopping mall/plaza)
Tired...rest as needed.
By working on HALT, you are avoiding those times or conditions that make us more vulnerable to having that first drink again.
So, rest or 'sleep' can actually be a very good thing.