Can cerebrospinal fluid deliver nutrients/drugs to neurons during sleep?
Only certain drugs can cross the blood brain barrier (BBB). However, there exist techniques to deliver drugs to the brain that otherwise cannot permeate through the BBB.
One such technique is called intrathecal delivery that injects drugs directly into the cerebrospinal fluid, avoiding the BBB problem and allowing the drug to reach cells, including neurons, in the brain. It has been used for certain kinds of chemotherapy, pain management, treatment of spastic cerebral palsy, and more recently for enzyme replacement therapy.
However with intrathecal delivery there is a risk of infection. 

Having said that, if a drug reaches the CSF then your hypothesis should be correct. There is no experimental evidence for it yet.