The short answer to this question is, "Yes, they can. It simply depends on how we define literature."
Cuddon defines literature as follows:
A vague terms which usually denotes works which belong to the major genres: epic, drama, lyric, novel, short story, ode.
Further down he adds:
However, there are many works which cannot be classified in the main literary genres which nevertheless may be regarded as literature by virtue of the excellence of their writing, their originality and their general aesthetic and artistic merits.
He then goes on to list works such as Aristotle's Poetics, Descartes's Discourse on Method, Gibbon's Decline and Fall of the Roman Empire, Darwin's On the Origin of Species and Lytton Strachey's Queen Victoria.
What Cuddon does not mention that the concept of literature changed around the beginning of the 19th century. In Chapter 2 of Literary Theory: A Very Short Introduction points out that
Prior to 1800 literature and analogous terms in other European languages meant 'writings' or 'book knowledge'. (...) And works that today are studied as literature in English or Latin classes in schools and universities were once treated not as a special kind of writing but as fine examples of the use of language and rhetoric. (...) Students were not asked to interpret them, as we now interpret literary works, seeking to explain what they are 'really about'. On the contrary, students memorized them, studied their grammar, identified their rhetorical figures and their structures or procedures of argument.
Based on this approach to literature, it would be perfectly normal to study the essays of Montaigne, Bacon and even Addison in what we now call a literature class, even though they don't fit the definition of literature given by Cuddon at the start of this answer. That definition reflects a concept of literature that originated in early 19th-century romanticism and that is restricted to imaginative writing. Culler cites Madame de Staël's On Literature Considered in Its Relations with Social Institutions, published in 1800, as an influential source of this conception, even though its roots go back to late-18th-century German romantics.  Based on this more restrictive definition of literature, essays would not be considered literature.
Baldick mentions an even more restrictive definition:
Even more restrictive has been the academic concentration upon poetry, drama, and fiction.
However, he immediately adds:
Until the mid-20th century, many kinds of non-fictional writing—in philosophy, history, biography, criticism, topography, science, and politics—were counted as literature; implicit in this broader usage is a definition of literature as that body of works which—for whatever reason—deserve to be preserved as part of the current reproduction of meanings within a given culture (unlike yesterday's newspaper, which belongs in the disposable category of ephemera). This seems more tenable than the later attempts to divide literature—as creative, imaginative, fictional, or non-practical—from factual writings or practically effective works of propaganda, rhetoric, or didactic writing.
The above definitions of literature attempt to use inherent characteristics as criteria for inclusion or exclusion but can't get around the observation that this is not always consistent with what we treat as literature (see e.g. Baldick's "works which ... deserve to be preserved ..."). As I discussed in a related answer, the definition of literature is something like the definition of "weed": weed is not a biological category, it is just a range of unrelated plants that we don't want in our gardens or our agricultural fields. So the question boils down to the following: Whether essays are literature or not depends on what types of text a specific culture treats as literature during a specific era. What we treat as literature has varied over time. During my school and university education, the essay has always been of secondary importance.
- Baldick, Chris: The Concise Oxford Dictionary of Literary Terms. Second edition. Oxford University Press, 2001.
- Cuddon, J. A.: The Penguin Dictionary of Literary Terms and Literary Theory. Third edition. Penguin 1992.
- Culler, Jonathan: Literary Theory: A Very Short Introduction. Oxford University Press, 1997.
 It would be an interesting question whether Germaine de Staël was influenced by those German romantics before 1800. During her exile she lived in Germany for some time and "travelled on to Berlin, where she made the acquaintance of August Schlegel who was lecturing there on literature", but that was after 1800.