Yes, I do think that one can exaggerate fan-ness especially about Tolkien's creation,
But - to defend languages a little 😛 ... I don't think that learning a language can in any way be an 'exaggeration' of interest, even less in a case like the Eldarin languages one can study without dedicating all day to it, without pressure, and that are so essential for the place they come from. And besides providing further information and understanding of their culture, learning a constructed or in this case fictional language / family of languages definitely improves one's abilty to get used to and learn other, 'real' languages, too, by offering more insight in how a language as a system actually works, how it's built up et cetera, even if that isn't its specific purpose, not having been designed as a logic language.
Beside that, the tongues of Middle-earth are art, and as some may find delight in music or painting or literature, others can simply enjoy a language per se, as a living system, as a vivid, breathing being, maybe finding pleasure in admiration of its superficial beauty, its fragile and idiosyncratic character hiding its overwhelming power and strength; others can marvel at the complex obscurities of intertwined cases and tempora, daydream adoring the undescribe- and unimitatable flowing sounds of the phonetic complexion of a people's philosophy and way of thinking.
Others can love languages.
And that is more than a good reason to try to understand them, I think 🙂
Maybe they are fanatics, radicals... but harmless ones 😛
As for your question - there are thousands of people learning Sindarin or Quenya; hardly anyone uses it for spoken communication though, after all it's no GA-language, but the product of excessive linguaphilia 😛