It doesn't work that way.
The real problem is lack of sleep. If you get adequate sleep, you will retain your ability to be attentive and to process information.
The whole attentional network, which is in the brain, shrinks and dims when you're fatigued or sleep deprived, and expands out to its full glory when you're well rested. You all know the difference. When you wake up after a good night's sleep, often simple solutions to problems that have been plaguing you reveal themselves.
Sleep is the essence. It's not rest. It's not time off. It's sleep. If you get seven or eight hours of sleep, you can work most of the rest of the time.