The closest thing we have to the 'Great American Novel' is The Adventures of Huckleberry Finn by Mark Twain. Twain did a lot of research into dialects when he wrote this book so educated people speak differently from farmers and farmers speak differently from slaves. All the characters are defined (somewhat) by how they speak.
Twain explains this in a foreword, hoping the reader won't think all the characters are trying to sound alike but failing. 8^)
I read this book in high school, before I understood the real diversity of 'Southern accents'. And I found it not just interesting but a lot of fun, and that it helped explain the differences between the characters.
It would be hard to do though. Every character has to be understandable to a general audience, so you can't use dialects that are too strange. Still, there would certainly be noticeable differences between a Brit and an Aussie, and you could have a lot of fun with that.