I've never watched Glee and didn't manage to get my hands on a video extract, but from the comments I saw on an article, it looks like that character is actually closer to being a drag-queen than a transsexual. Even though here, both are under the term "transgender", for the general public, transgender = transsexual, or transsexual who can cope with their genitals.
If the comments are accurate, I find it unfortunate that the writer would pick the most stereotypical/caricatured "version" of a transgender, the one the easiest to disregard/not take seriously, and (I think?) the one the most versed in aesthetical worries rather than deeper issues, and the one that lives the least gender dysphoria.
Again, if the people who commented were right... I'm not sure I actually want that kind of visibility. I mean, everyone has been knowing what a drag-queen is for decades, and it's a well-accepted fact that many (not necessarily most) do it as a hobby or means of living, not remotely as a means to relieve any sort of psychological anguish.
I don't think that iif one day, when I come out to someone and they say "oh, I know, I saw the episode with Unique on Glee!" I'll be happy that they saw that episode.