Not if the notes were written for a particular person. If Dumbledore writes a note for Harry, and Moody delivers it, then it is Dumbledore that has divulged the secret. If Moody reads the letter, assuming he was already in on the secret, then it remains a secret. If Moody reads the letter to Tonks, assuming she was already in on the secret, then it remains a secret. Yet because he was not the master of the secret, Moody would have been unable to pass the note on to say...Lavender Brown. Either his arm would not move, or the parchment would not unfurl, or whatever, but it wouldn't be possible.