I think a letter would be too much. No matter how much I admire a celebrity, I guess I wouldn't have the idea or the guts of writing and sending an actual letter that details how much I admire him, or how he inspires me on so many levels.
Personally, the closest thing to a letter that I actually have done is to send a private message on Instagram. Of course, this is not even a random message but a comment to a post to which I just mentioned (in passing) how his journey towards success made me change my view of life. Sadly, I did not get a response.
If you plan on writing a letter to a celebrity, there is nothing wrong with that. We are all free to express ourselves. However, do not expect that you will receive something of equivalent effort, as most celebrities are really not too responsive.