Quite obviously, if they don't have language they will not acquire language from books. The gap between not having and having language is simply too great. Therefore I will assume that they already have language, and I will concentrate on the possibility of learning a foreign language from books.
Second, simply learning a foreign language from books is well-known to be possible. After all, there are many millions of people on Earth who can read Latin, or Ancient Greek, or Biblical Hebrew; and there are quite a few people who can read Sumerian, or Akkadian, or Hittite, or Ancient Egyptian. Those languages do not have any native speakers, and everybody who can read them has learned to read them from books.
Moreover, languages such as Hittite or Tocharian were deciphered from written materials without the benefit of any Rosetta stone or other dual-language inscriptions; so we know that it is possible, in special circumstances, to acquire an unknown language based only on written materials in that language.
This answer will concentrate on the possibility of learning the spoken form of a language based only on written materials.
In fiction
Famously, E. R. Burroughs's Tarzan of the Apes learned written English from the books he found in the ruins of the cabin built by his deceased father. Of course, he had no way of learning to speak English, since his knowledge was limited to the written form.
(The novel is freely available in multiple formats at Project Gutenberg.)
Actually there is a nice sequence in the book delving upon the difference between the spoken and written language. One of the first "civilized" persons Tarzan met was a Frenchman, lieutenant Paul D'Arnot:
D'Arnot spoke to him in French, but the man only shook his head—sadly, it seemed to the Frenchman.
Then D'Arnot tried English, but still the man shook his head. Italian, Spanish and German brought similar discouragement.
D'Arnot knew a few words of Norwegian, Russian, Greek, and also had a smattering of the language of one of the West Coast negro tribes—the man denied them all.
After examining D'Arnot's wounds the man left the shelter and disappeared. In half an hour he was back with fruit and a hollow gourd-like vegetable filled with water.
D'Arnot drank and ate a little. He was surprised that he had no fever. Again he tried to converse with his strange nurse, but the attempt was useless.
Suddenly the man hastened from the shelter only to return a few minutes later with several pieces of bark and—wonder of wonders—a lead pencil.
Squatting beside D'Arnot he wrote for a minute on the smooth inner surface of the bark; then he handed it to the Frenchman.
D'Arnot was astonished to see, in plain print-like characters, a message in English:
I am Tarzan of the Apes. Who are you? Can you read this language?
D'Arnot seized the pencil—then he stopped. This strange man wrote English—evidently he was an Englishman.
"Yes," said D'Arnot, "I read English. I speak it also. Now we may talk. First let me thank you for all that you have done for me."
The man only shook his head and pointed to the pencil and the bark.
"Mon Dieu!" cried D'Arnot. "If you are English why is it then that you cannot speak English?"
And then in a flash it came to him—the man was a mute, possibly a deaf mute.
So D'Arnot wrote a message on the bark, in English.
I am Paul d'Arnot, Lieutenant in the navy of France. I thank you for what you have done for me. You have saved my life, and all that I have is yours. May I ask how it is that one who writes English does not speak it?
Tarzan's reply filled D'Arnot with still greater wonder:
I speak only the language of my tribe—the great apes who were Kerchak's; and a little of the languages of Tantor, the elephant, and Numa, the lion, and of the other folks of the jungle I understand. With a human being I have never spoken, except once with Jane Porter, by signs. This is the first time I have spoken with another of my kind through written words.
Tarzan then learns the "language of men" from the Frenchman, innocently associating the French spoken words with the English written words:
And so D'Arnot commenced at once, pointing out familiar objects and repeating their names in French, for he thought that it would be easier to teach this man his own language, since he understood it himself best of all.
It meant nothing to Tarzan, of course, for he could not tell one language from another, so when he pointed to the word MAN which he had printed upon a piece of bark he learned from D'Arnot that it was pronounced "homme", and in the same way he was taught to pronounce APE, "singe" and TREE, "arbre".
Fortunately, lt. D'Arnot realized his mistake and eventually Tarzan learned both spoken English and spoken French.
In reality
The following real-history examples show the difficulty of reconstructing a spoken language from written materials only.
The first example is the reconstruction of older forms of Chinese. The Chinese language(s) have always been written with their infernal characters, so we (for suitably chosen meanings of the word "we") can understand texts written in Old and Middle Chinese; the problem is that Chinese characters do not have any direct relationship with the sounds made by a human speaking the language, to the effect that reconstructing the spoken form of the language is a very difficult problem.
Old Chinese was spoken until well into the first millennium BCE, and evolved into Middle Chinese. For comparison, consider that we have much less trouble reconstructing the spoken form of Homeric Greek, which is roughly of the same time depth; the difference being that Greek was written alphabetically, with a script which represented the sounds of the words and which was never forgotten.
(Middle Chinese, spoken up to the middle of the 1st millennium CE, is a little easier to reconstruct because we have some materials describing some aspects of the pronunciation of words, mostly for the purpose of enabling writing formally correct poetry; the problem remains very difficult, but at least it's not hopeless.)
The end result is that we have multiple concurrent attempts to reconstruct the sounds of Old Chinese, reconstructions which are only slowly coalescing into a fuzzy consensus. Remember that this is about a language which has living descendents spoken by a billion people!
The second example is about the Hittite language, spoken in Asia Minor (modern Anatolia, in Turkey) around the middle of the 2nd millennium before the common era. The decipherment of Hittite by Bedřich Hrozný is a fine story in itself, but it remains for another time. What's interesting in the context of this question is how many holes are in our ability to reconstruct spoken Hittite.
Hittite was written with the Akkadian cuneiform script, so that for the most part we know how it sounded. The problem is that in their script the Hittites used quite a few Sumerograms, which represented common words without any link to the spoken form. (Think how in English we use symbols such as 7, &, %, $, and then imagine that we never wrote seven, and, percent or dollar.)
For example, we have not found any Hittite text containing the word for "horse" written phonetically; in all the texts in which it appears it is written with a Sumerogram. The end result is that while we can read Hittite texts, there are quite a few common words which we have no idea how they sounded.
A ray of hope
As we see, it is very hard to reconstruct the spoken form of a language when all one has are texts written in a script which does not represent the phonetics of the language. If the script does represent the phonetics of the language, even as imperfectly as English script, and if the script was not forgotten, then the problem becomes tractable.
For example, there are no native speakers of Ancient Greek, or Latin, or Biblical Hebrew; but those languages were written with scripts which represented the phonetic reality, and the scripts themselves were never forgotten. We can be pretty confident that our reconstructions of the spoken forms of Ancient Greek, or Latin, or Biblical Hebrew are good enough.
Even when the script was forgotten, there is a ray of hope if the script reflected the pronounciation and the language left known descendants; for an example, consider Ancient Egyptian. While the reconstructions of the spoken forms of Ancient Egyptian are extremely imperfect and quite approximative, they are nevertheless light-years ahead of the reconstructions of Old Chinese. (The main problem is that Ancient Egyptian script, like all Semitic scrips, does not represent the vowels; so that while the consonants are pretty well reconstructed, the actual pronunciation is still quite fuzzy.)
And Ancient Egyptian also provides an example of a way out. Since the actual pronunciation of the words is uncertain, almost nobody attempts to use it. People who study Ancient Egypt have developed a conventional pronunciation, which, while known to be wildly different from the sounds made by the ancient Egyptians themselves, is good enough to enable communication between Egyptologists.
For example, the name twt-ꜥnḫ-ı͗mn is conventionally pronounced /tuːtənˈkɑːmən/ in English, but, in his lifetime, it was likely to be pronounced something like *[taˈwaːt ˈʕaːnxu ʔaˈmaːn]. (Wikipedia, s.v. Egyptian language; the name in question is of course "Tutankhamun".)
In conclusion
In the absence of some form of direct transmission of the phonetic information, the species in question won't be able to reconstruct the pronunciation of English. They will be able to learn written English, and they will be able to develop a conventional pronunciation for use in speech. As a wild speculation, they may pronounce "famously, E. R. Burroughs's Tarzan of the Apes learned written English from the books he found" as "'senaifru 'o 'ol 'tillaibʱfof 'kelvem as kʰo 'eudof 'ro:lmog 'hlukkom 'ombruʒ slan kʰo ta:pf ho saimg"...
