It's well known that sleep is an absolute requirement for athletes. If you don't get an optimal amount, performance will suffer: http://sportsmedicine.about.com/cs/conditioning/a/aa062800a....
Athletic activity causes actual physical microdamage that takes rest time, nutrition, and hormones to repair. The elevated secretion of human growth hormone during REM sleep is a significant reason why athletes perform better on more sleep.
No such analogue exists for the human brain. Mental activities, at worst, deplete neurotransmitter levels. I have seen no evidence to suggest that massive dosages of sleep do a better job of restoring these levels than minimally adequate amounts.
The systems of the body are not neatly partitioned into modules.