I am almost a layman but I got to learn something on the subject.
As far as I could understand, what in common can be found in wake/sleep and learning are the brain waves. Neurons exchange signals in form of electrical pulses and the collective frequency of these firing rates are indeed these brain waves. In this article it is pointed out that learning can be differentiated in explicit and implicit.
Explicit learning occurs, for example, as one is engaged in learning English grammar rules (that posted article explains more in deep the difference between explicit and implicit learning) This kind of learning is characterised by the dominance of high frequency brain waves (called alpha and beta, the latter being faster. This range is characterised by frequencies of 10-30 hertz. Hertz is a measure of frequency, defined as $1/second$, that is: consider for example the centrifugue of the washing machine: if it does 10 rounds in a second, then its frequency is 10 hertz).
On the other hand, when one sleeps, his/her brain wave frequency drops from alpha to theta in the pre-sleep stage and eventually to delta in the deep sleep phase. This latter is the slowest frequency of the spectrum (ranging in 1 to 4 hertz according to refer here for more).
Hence I would say that active learning as could performed during wake can not be accomplished during sleep inasmuch there is not the proper brain waves setting to, almost for what concerns explicit learning.
I hope it helps and hope I got the point correctly. Wish you best luck with your study!