If the title of your question means to you what it literally means, the answer is, plainly, 'NO'. Just by observing written texts, without any access at all to the extralinguistic referents and contexts of use of the written expressions, you would be absolutely unable to determine either their 'sound' or their 'meaning' (/use), and you would have no grounds at all to call that set of inscriptions 'English' or anything else, or even less to say that you had learnt English.
Of course, you could study the distribution of each of the symbols figuring in your necessarily finite collection of inscriptions and, with a lot of patience, eventually establish an 'alphabet' (an exhaustive list of the symbols in them) and a set of 'construction rules' for the observed subset of L, i.e., a syntax (in the broad sense) in which you specified the observed combinations of 'letters' (a sort of 'phonotactics' of L), an inventory of (observed) recurring 'morphs' (bits of 'words' observed to systematically recur in identifiable co-texts), an inventory of observed 'words' (assuming the inscriptions contained punctuation marks, e.g., spaces, something to separate sentences), and you could, on distributional grounds, establish a finite set of 'syntactic categories' of words, and, since your corpus would be, by definition, a closed one, a finite set of recurring patterns of combination of categories of 'words' into 'phrases' and 'sentences', i.e., you could surely reach a fairly detailed set of hypotheses about the 'syntax' of L in the narrow sense, too.
But, without access to the extralinguistic correlates of such 'words', 'phrases' and 'sentences', your 'language' L would have no 'semantics', would thus not even be a 'semiotic' system (in Morris' sense), and, of course, you would not have learnt a human language at all, because what defines human languages is their capacity to 'recursively' correlate indefinitely complex 'forms' with their corresponding 'meanings' (= in Chomsky's terms: infinite use of finite means). On the contrary, by definition, all the written expressions of L you could collect, however large your 'corpus' were, would only constitute a tiny fraction of what the alphabet and the rules of construction would be able to 'generate'.
But, above all, your L would not be a system of 'signs'. Hence, even if you learnt your 'alphabet' and your 'construction rules' to perfection, even if you subsequently generalized and extrapolated your 'grammar' in order to 'generate' a much bigger complementary set of non-observed, but grammar-compliant and hence predictable new possible 'inscriptions', you would not be entitled to say you had learnt English (or any other human language).
The well-known cases in which such sets of inscriptions have been 'deciphered' could occur at all because the decipherers did eventually obtain at least indirect access to what the inscriptions and their parts 'referred to' and 'meant' (with all the caveats that philosophers of language since Quine have established in this respect). Without such direct or indirect access to the extralinguistic correlates of 'inscriptions' and their components, it would have been imposible to even decipher the observed expressions, let alone learn the underlying languages.