What you have here is a hypothesis and it's almost impossible to answer this conclusively because you can't design a randomized study but only look at correlations. In addition, "narcissism" itself is far from a simple concept and used differently by different researchers. For instance some see is as synonymous with self-esteem and self-confidence, some don't.
In fact, your view is closer to some of the psychoanalytical views of homosexuality. For instance, a hundred years ago, in talking about narcissism and abnormal development, Freud suggested that people who had experienced problems during libidnal development (libido is a kind of instinctual sexual energy behind our psychological development), including gays and "perverts", instead of choosing their mother as their "love-object", they'd use themselves as the love object. He labeled this abnormal sexual development a kind of narcissism. The theory is more complex than that but I just wanted to give you an idea of the kind of views I was referring to.
Contemporary research does not follow this line of thinking nor talks about development, gays or not, in those terms. In fact many (not all) psychoanalytical concepts are no longer seen as scientific (=falsifiable) so they're not seriously studied these days in universities. You would instead find researchers look, for instance, at homosexuality and mental health (with a lot of attention paid to social factors; see Herek & Garnets, 2007), but not studies of narcissistic development in homosexuals, except a couple here and there in psychoanalytical journals.
I took a look and most recent study I found in a non-psychoanalytical journal was by an Israeli researcher, Rubinstein, published in 2010. In her study she found exactly what she believed based on Freudian conception, that gays were more narcissistic but had less self confidence than heterosexuals.
As the invited commentary on that study (Hartmann, same issue, can't find citing info) mentions, given that there is still stigma against homosexuals, one need a higher standard for offering the conclusion that she had (the study used only 200 Jewish students in their 20s living in Israel and within what Hartmann calls "forceful social and religious traditions", and had relied on self-report, which is far from objective). In her defense, Rubinstein did talk about three potential interpretations and also the limitations of her study.
Some psychoanalysts believe that homosexuals are more narcissistic than heterosexuals but no good data is available to confirm that, partly because researchers try to be careful when they study sexual orientation because of potential misuse of findings, but more importantly because those conceptions of homosexuality are no longer seen as scientific or more useful/productive than current biological or psychological theories of homosexual development.
I hope you found this answer helpful.
Freud, S. (1957). On narcissism: An introduction. In J. Strachey (Ed. and Trans.),The standard edition of the complete psychological works of Sigmund Freud (Vol. 14, pp. 67–104). London: Hogarth Press (Original work published 1914).
Herek, G. M., & Garnets, L. D. (2007). Sexual orientation and mental health. Annual Review of Clinical Psychology, 3, 353–375.
Rubinstein, G. (2010). Narcissism and Self-Esteem Among Homosexual and Heterosexual Male Students. Journal of Sex & Marital Therapy, 36:24–34.