I assumed zipping to be determinative and that a standard gzip would lead to a "known" hash, ergo the idea to create a unknown zip file by adding some bytes.
It would be determinative only if all the header fields[1] stayed identical. A change in something like file name or mod time, would change the hash of the zipped archive without affecting the hash of the actual file.
I don't think you can expect the file mod time to be identical, as it isn't preserved through many forms of file distribution.
Also, you wouldn't need add a file. Zipping it alone would be enough to change the hash.