I believe the only difference between the GA645 and the GA645i is the i can read Fuji film bar codes and it has a second shutter button. If the bottom plate is the same then the GA bracket should fit. I do not have the i so I cannot tell you for sure.
I do have a GA645 and a GA645zi and a GA bracket and can tell you the GA bracket does not fit the GA645zi.
Thanks, Rich. Hoping to pick up a second GA, and wanted to verify which accessories will pull double-duty. Might pass over the ZI because of this. Thanks!