No, I think Uncle Bud won't tell Xaafuun because he most likely will knowing that in the story he already told her information. Also knowing his personality.  I think that he would not  tell Xaafuun because I think he is smarter than Uncle Bud but even though he is naughty he usally finds a way out of whatever trouble he is in. For example when he gets in trouble with Sargent Webb have you noticed that he might get in little trouble but he always goes home unharmed. In a way I think Uncle Bud is really smart in certant situations. For example when he decided not to jump on the train at the beggining of the story because it was for the Military or Army. But I think that Jack would have a sense to not tell.