[bayindirh]

I don't think so.

Sometimes modification time of a file which is not downloaded on computer A, but modified by computer B is not reflected immediately to computer A.

Henceforth, backup software running on computer A will think that the file has not been modified. This is a known problem in file synchronization. Also, some applications modifying the files revert or protect the mtime of the file for reasons. They are rare, but they're there.