Ok, let's just say that we don't really know. That would be the best answer. However, in my opinion, some peasants can read.
I think you are right on the fact that ex-nobles and nobles alike would be the first target of teh confiscation as they will be mostly literate.
Some as in how many? Considering the cost of the books, the learning, the materials, the opportunity cost, chances are really low for peasants be able to read. Let's say that 10% of the peasants were able to read, then it was even less likely for them to access to a book. let's say 5 of the 10% had access to books, then it was even less likey for them to get hold of one. Let's say 1% got hold of a book, would they had kept the books once the decree was issued?
Consider it took lots and lots of money to learn how to read, wouldn't people consider the cost of their lives vis-a-vis to that of a book when the decree was issued? Qin law was infamously strict. Would people of lower status in the society risk their lives to preserve the said books? Most likely they would turn in the books willingly.
People who withheld the books were mostly ex-nobles whose states were conquerd by Qin and that they were not Qin's supportors. Withholding a book is like withholding a Masamune sword during Tokugawa's reign, a symbolism. All in all, the chances for the ancient books, subjected to confication, to survive in originality were really low.