Is there a study that proves that people with messy or fast handwriting have a high IQ?
Not that I know of. As far as I know, fast handwriting that ends up shortcut-y to the point of illegibility is mostly associated with amount of handwriting experience. Spend a few decades doing a lot of writing by hand and your handwriting will look like that.
And then there's dysgraphia, which I'm not aware of being correlated with intelligence either way.