As an individual case maybe, but:
1. Alcohol still in the system after a period of sleep (especially a short period after significant drinking) is a well-known issue and has been the subject of publicity campaigns (e.g. http://news.bbc.co.uk/1/hi/uk/7801933.stm. Any responsible driver should be aware of the possibility of still being over the limit the mornig after.
2. Driving whilst tired is also a well-known issue and should be avoided as it significantly impairs your ability.
3. Being "drunk" is not necessary for the excess alcohol ofence - that is an absolute offence regardless of it's visible effect on you. There is another, more serious offence specifically addressing driving whilst drunk (or drugged).
