Can "et al." be applied to one entity?

If a referenced paper has two authors X and Y, can et al. be applied in this case? For instance, is X et al. correctly used?

It would be an odd use of the term.

The abbreviation et al., for Latin et alii, means "and others" (plural).

From Latin, abbreviation of et (“and”) and alii (“others”) (English: et alii) and its forms and derivatives. (Wikitionary)

It is used to avoid your sentence turning into a list of referenced authors, however when you have only two authors this is not an issue.

For instance the APA style guide does not make use of the term for just two authors with in-text citations, as explained on the APA style blog:

First citation : Palmer & Roy, 2008

Second and subsequent : Palmer & Roy, 2008

Compared with three, four or five authors:

First citation: Sharp, Aarons, Wittenberg, & Gittens, 2007

Second and subsequent: Sharp et al., 2007

and six or more:

First citation: Mendelsohn et al., 2010

Second and subsequent: Mendelsohn et al., 2010.

Whereas the Chicago Manual of Style, prescribes the Author-Date system for in-text citations, as follows:

(Pollan 2006) author last name, year of publication; cites whole work

(Mnookin and Kornhauser 1979, 22) two authors, year, page number

(Jones, Smith, and Chao 2008, 118-119) three authors, year, page number range

(Barnes et al. 2008) four or more authors uses only first author.

Also the Merriam-Webster definition asserts you would typically use it to stand for two or more names:

Et al. typically stands in for two or more names, especially in bibliographical information. It's preceded by a comma only when more than one name is listed (as in cases in which two or more texts are authored by the same person or by people with the same surname):

The book by Carson et al. is regarded as the authoritative text on the topic.

The article by Jones, Perez, et al. is well-known, but the one by Jones, Lee, et al. has been more widely cited.

Also on a general matter of principle, if two authors have created a work or idea you are referencing it's just to refer to both of them. When you have many authors this hampers the readability of your paper, but if this is not an issue, no need to relegate one of them to a footnote in your paper!