That's Foucault's theory, but Rictor Norton's book I linked to convincingly debunks Foucault as ideological and ahistorical. Quoting an excerpt, here are historical cases of unmarried men going for each other instead of marriage and children:

In between these two extremes of lust and idealism we find a sense of identity based upon ordinary and unremarkable same-sex love. The records of the Inquisition in Spain, Portugal and Brazil; the police archives of early eighteenth-century Paris; the records of the Officers of the Night of sixteenth-century Venice – all clearly document a preponderance of men who were bachelors and who preferred their own sex. Statistical analysis of the particularly full and detailed Florentine records ‘of the marital status of the men incriminated for sodomy from 1478 to 1483 reveals that fully three-fourths of all such men aged nineteen to seventy were unmarried.

These guys sound like they are exclusive, obligate homosexuals.

As for identity, just because the historical labels for queer people were negative, it does not mean that those terms were just externally-imposed slurs, and that homosexual identities did not exist:

In Foucault’s famous statement: ‘Homosexuality appeared as one of the forms of sexuality when it was transposed from the practice of sodomy onto a kind of superior androgyny, a hermaphroditism of the soul. The sodomite had been a temporary aberration; the homosexual was now a species.’ He ludicrously dates this shift to 1870. But the men discussed in the preceding paragraph had a sense of themselves that transcended both ‘the practice of sodomy’ and ‘temporary aberration’. In fact Dutch sodomites in 1734 were described by contemporaries as ‘hermaphrodites in their minds’ (Boon 1989) – an exact match for Foucault’s ‘hermaphroditism of the soul’. The concepts of masculine homosexual women and effeminate homosexual men dominated the premodern world. The homosexual was considered an androgynous species in Aristophanes, in Juvenal, in all the ancient literature about the transgendered priests of Cybele in the ancient and classical world. It was not a modern construct.

The truth is that a homosexual category existed many centuries prior to the nineteenth century. There are literally scores of fifteenth-century Italian authors who portray homosexual characters rather than homosexual incidents (G. Dall’Orto, ‘Italian Renaissance’, EH), and it is a nonsense to label such sodomites ‘temporary aberrations’ rather than members of a species. In real life there is the famous example of self-labelling, the painter Antonio Bazzi (1477–1549) who was proud of his nickname ‘Il Sodoma’. According to his contemporary Vasari ‘he did not take [it] with annoyance or disdain, but rather gloried in it, making jingles and verses on the subject, which he pleasantly sang to the accompaniment of the lute’.

Rictor Norton is a widely published queer historian, his research goes back centuries, and seems very solid. I think we should go with his account and toss Foucault's social constructionism.