Quite the opposite, I try hard to keep my brain working while dozing off and while waking up .. and as much as possible when I am drifting in and out from consciousness, because sometimes that's how I find a solution to a problem that I have been banging my head against the wall for. I think there was some research done before about the upside of some truth behind "I'll sleep on it".
I have a hard time switching my brains off. Even when i try to sleep. The problem is that having this ability is what gives me my technical abilities so its both a blessing and a curse.