There's a difference between changing the file and replacing the file. According to this Microsoft page on Hard Links and Junctions, "Any changes to that file are instantly visible to applications that access it through the hard links that reference it." However, consider what happens when you replace a file: the file system deletes the file (in this case the hard link), then writes the new file with the same path and file name as the former hard link.
So it depends on how the program you're using to change the file writes to the file system when it updates the file.
See also What operations breaks the hardlinks