Yeah, I think it's safe to say that most are familiar with the suit, even if they only know him from the movies. That's how Wolverine appears on toys, video games, cartoons, and just about every form of merchandise. Even the Wolverine Halloween costume, which was the yellow suit, had an Origins logo, despite the suit never appearing in the movie.
I'm still leery of how Hugh would look wearing it. But I'd love to see some variation of it in a movie. That would be cool.