Maybe, but it comes to depend on choice of terminology. As I have frequently seen it defined, it'd be sex dysphoria (or genital, as calicarly suggested, which strikes me as interchangeable).
That's from the school of terminology where there's sexuality (who you're attracted to), gender identity (how you identify internally), gender expression (how you present yourself socially), and biological sex (which parts you have).
I'm not sure how this would fit in terms of clinical / DSM terminology, but I think it's exactly the case where distinguishing gender identity from biological sex is important. That's probably also the rationale that would be used to deny surgery in such a case. I am not saying I agree with it, but I think the argument would be that GRS is intended to bring biological sex in line with gender identity, the latter of which is a well established condition. I suspect there's little documentation of sex/genital dysphoria as "real," which may be why doctors would be hesitant to treat it. (Scare quotes, of course, because I am not decidedly not questioning the reality of the condition, but a doc might.)