Will Wheaton, the actor who played Wesley Crusher is very open about the fact that he is a nerd, and a fan of the original series. He's written himself numerous times about his experiences being a fan while also being on the show, such as on this Facebook post where he mentions he was attending Star Trek conventions long before he was ever asked to be a guest at one.
I have found a number of sources where the fact that he was a fan of the original series before he was cast as Wesley Crusher is pretty strongly implied, such as in this interview where he had said of his audition for the role of Wesley Crusher:
It's kind of intimidating meeting Gene Roddenberry—it was like meeting
Arthur C. Clarke or somebody—but he was a great guy, and I ended up
getting the job.
Another quote from an interview with him done regarding the remastered Star Trek: The Next Generation Blu ray:
Most, at first, thought that he was the luckiest 15-year-old in the
galaxy, able to work with greats like Patrick Stewart in a sequel of a
series that he was both a fan of and that already had large fan
In addition, I've found a youtube video of an interview with Wil Wheaton that is said to have been recorded before Star Trek: The Next Generation has aired, in which is said:
Narrator: Born after the original series went off the air, Wil
Wheaton, the youngest member of the cast of Star Trek The Next
Generation considers himself, without a doubt, to be a fan.
Wil Wheaton: I'm a Trekkie, but not the kind of Trekkie that knows
everything about the show. I couldn't tell you like who starred in
episode number 13, you know, in the second half, who was the main
focus, or anything like that. Um, what I do is I like to read the
books. The novels I haven't really gotten into yet. But like the
comic book I read, the old series I watch every night, unless I have
to get up real, real early for work the next day.
Finally, I cite a definitive quote from Wil Wheaton's own blog, where Wil Wheaton refers to playing Star Trek as a kid, nearly ten years before he got his role on The Next Generation:
When I was a little kid, playing Star Trek on the playground (I always
ended up being Spock), I had no idea that less than a decade later it
would become a fundamental part of the tapestry of my life.