No. But it’s not necessarily less active either.
@marinelife – I’m not sure about the validity of the link you provided. Did you see the “About HS” section?
First of all, when we refer to brain activity, what do we mean? Electrical activity measured by an EEG? Use of glucose and oxygen? Number of neurons firing in the neocortex?
When it comes to the human brain a lot of myths are being floated around, like Einstein’s
http://en.wikipedia.org/wiki/10_percent_myth
Scientists have already learned a great deal about sleep and memory consolidation. You can find good articles about it here
http://scholar.google.com/scholar?q=sleep+hippocampus+memory&hl=en
Sleep seems critical for learning.