No, the fseek() is necessary - after writing to the file, the file pointer (I'll use "file pointer" to refer to the current position in the file, the thing you change with fseek()) is at the end of the file, and reading at the end of the file gives you EOF right away, which manifests itself as an empty upload.
Where you might be getting confused is in some systems' requirement that one seek or flush between reading and writing the same file. fflush() satisfies that prerequisite, but it doesn't do anything about the file pointer, and in this case the file pointer needs moving.
-- Josh